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Microwave Quantum Memcapacitor Effect
Published 12 Nov 2023 in quant-ph and cond-mat.supr-con | (2311.06925v2)
Abstract: Developing the field of neuromorphic quantum computing necessitates designing scalable quantum memory devices. Here, we propose a superconducting quantum memory device in the microwave regime, termed as a microwave quantum memcapacitor. It comprises two linked resonators, the primary one is coupled to a Superconducting Quantum Interference Device, which allows for the modulation of the resonator properties through external magnetic flux. The auxiliary resonator, operated through weak measurements, provides feedback to the primary resonator, ensuring stable memory behaviour. This device operates with a classical input in one cavity while reading the response in the other, serving as a fundamental building block toward arrays of microwave quantum memcapacitors. We observe that a bipartite setup can retain its memory behaviour and gains entanglement and quantum correlations. Our findings pave the way for the experimental implementation of memcapacitive superconducting quantum devices and memory device arrays for neuromorphic quantum computing.
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[10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. 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Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). N. K. Upadhyay, H. Jiang, Z. Wang, S. Asapu, Q. Xia, J. J. Yang, Emerging Memory Devices for Neuromorphic Computing, Adv. Mater. Technol. 4, 1800589 (2019). [5] W. Millar, Some general theorems for non-linear systems possessing resistance, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 42, 333 (1951). [6] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957). [7] Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). W. Millar, Some general theorems for non-linear systems possessing resistance, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 42, 333 (1951). [6] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957). [7] Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957). [7] Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. 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Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. 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Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957). [7] Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. 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Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). 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Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957). [7] Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Biolek, D. Biolek, and V. Biolková, Interpreting area of pinched memristor hysteresis loop, Electron. Lett. 50, 74 (2014). [8] L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. 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Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. 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Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. Chua, Memristor-The missing circuit element, IEEE Trans. Circuit Theory 18, 507 (1971). [9] D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. 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Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. 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Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. 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Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. 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[51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature 453, 80 (2008). [10] Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. 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DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. 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Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. 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W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. 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Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. 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Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. V. Pershin, and M. Di. Ventra, A simple test for ideal memristors, Journal of Physics D: Applied Physics, 52, 1 (2018). [11] M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. 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Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. 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Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. 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Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. 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A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. 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Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. 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Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. 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Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. 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Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. 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Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. 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Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). 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- M. Di Ventra, Y. V. Pershin, and L. O. Chua , Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors, Proc. IEEE 97, 1717 (2009). [12] Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Yin, H. Tian, G. Chen, and L. O. Chua , What are Memristor, Memcapacitor, and Meminductor?, IEEE Trans. Circuits Syst. II Express Briefs 62, 402 (2015). [13] S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. 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Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. 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Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Park, H. Jeong, J. Park, J. Bae, and S. Choi, Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing, Nat Commun 13, 2888 (2022). [14] J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. William, “Memristive” switches enable “stateful” logic operations via material implication, Nature 464, 873 (2010). [15] Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing, Nat. Mater. 16, 101 (2017). [16] Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. 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Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. 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DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. 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Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. 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W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. 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Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Y. Li, Z. Wang, R. Midya, Q. Xia, and J. J. Yang, Review of memristor devices in neuromorphic computing: materials sciences and device challenges, J. Phys. D: Appl. Phys. 51, 503002 (2018). [17] F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. 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Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. 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Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. 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Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. 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Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. 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L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. 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- F. M. Bayat, F. M. Bayat, M. Prezioso, B. Chakrabarti, H. Nili, I. Kataeva, and D. Strukov, Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits, Nat. Commun. 9, 2331 (2018). [18] Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. 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Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Wang et al., Reinforcement learning with analogue memristor arrays, Nat. Electron. 2, 115 (2019). [19] Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Z. Liu et al., Neural signal analysis with memristor arrays towards high-efficiency brain-machine interfaces, Nat. Commun. 11, 4234 (2020). [20] M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Lanza, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication Science. 376, 6597(2022). [21] A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. 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Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. 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Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. 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Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020). [22] S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. 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[28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. 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Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. J. Kim, S. Kim, and H. W. Jang, Competing memristors for brain-inspired computing, iScience 24, 101889 (2021). [23] S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. 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L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kundu, P. B. Ganganiak, J. Louis, H. Chalamalasetty, and B. P. Rao, Memristors Enabled Computing Correlation Parameter In-Memory System: A Potential Alternative to Von Neumann Architecture, IEEE Trans. VLSI Syst. 30, 755 (2022). [24] P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016). [25] S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. 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Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). 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Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko, Y. V. Pershin, and F. Nori, Qubit-Based Memcapacitors and Meminductors, Phys. Rev. Appl. 6, 014006 (2016). [26] S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. 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Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. N. Shevchenko and D. S. Karpov, Thermometry and Memcapacitance with a Qubit-Resonator System, Phys. Rev. Appl. 10, 014013 (2018). [27] S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Peotta and M. Di Ventra, Superconducting Memristors, Phys. Rev. Appl. 2, 034011 (2014). [28] J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. 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Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. 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Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. 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Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
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Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017). [29] M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. 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Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. 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W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. 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Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. 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Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Sanz, L. Lamata, and E. Solano, Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018). [30] T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Gonzalez-Raya, J. M. Lukens, L. C. Céleri, and M. Sanz, Quantum Memristors in Frequency-Entangled Optical Fields, Materials 13, 864 (2020). [31] M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. 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Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, F. Ceccarelli, A. Crespi, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nat. Photon. 16 318–323 (2022). [32] D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. 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Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). D. Marković and J. Grollier, Quantum neuromorphic computing, Appl. Phys. Lett. 117, 150501 (2020). [33] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. 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Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). 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V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning, Phys. Rev. Applied, 8, 024030 (2017). [34] K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). K. Fujii and K. Nakajima, Quantum Reservoir Computing: A Reservoir Approach Toward Quantum Machine Learning on Near-Term Quantum Devices, Natural Computing Series, Springer, Singapore, 423–450 (2021). [35] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. 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Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. 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[51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, X. Chen, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021). [36] S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. 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Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. 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[41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. 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Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). 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Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. 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[40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V. 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Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
- S. Kumar, F. A. Cárdenas-López, N. N. Hegade, F. Albarrán-Arriagada, E. Solano, and G. A. Barrios, Tripartite entanglement in quantum memristors, Phys. Rev. Applied 18, 034004 (2022). [37] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE. 64, 209 (1976). [38] M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. 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Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. 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W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). 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H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. 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Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). 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Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. 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Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
- M. Di Ventra and Y. V Pershin, On the physical properties of memristive, memcapacitive and meminductive systems., Nanotechnology, 24, 255201 (2013). [39] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn, 12, 570 (1957). [40] U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl., 45, 897 (2017). [41] A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. Parra-Rodriguez, Algebraic canonical quantization of lumped superconducting networks, Phys. Rev. B, 106, 024510 (2022). [43] R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Dynamical Casimir effect in superconducting microwave circuits, Phys.Rev. A 82, 052509 (2010). [44] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376(2011). [45] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77–80 (2012). [46] G. de Lange, D. Risté, M. J. Tiggelman, C. Eichler, C. Eichler, L. Tornberg, G. Johansson, A. Wallraff, R. N. Schouten, and L. DiCarlo, Reversing Quantum Trajectories with Analog Feedback, Phys. Rev. Lett. , 112, 080501 (2014). [47] S. Lloyd and J. J. E. Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Canonical circuit quantization with linear nonreciprocal devices, Phys. Rev. B, 99, 014514 (2019). [42] I. L. Egusquiza and A. 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Slotine, Quantum feedback with weak measurements, Phys. Rev. A 62, 012307 (2000). [48] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. 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Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys.Rev. Lett. 109, 193602 (2012). [49] T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). T. Yoshioka, H. Mukai, A. Tomonaga, S. Takada, Y. Okazaki, N.-H. Kaneko, S. Nakamura, and J.-S. Tsai, Active Initialization Experiment of Superconducting Qubit Using Quantum-circuit Refrigerator, Phys. Rev. Applied 20, 044077 (2023). [50] M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. 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Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). M. Di Ventra and Y. V. Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nanotechnology 24, 255201 (2013). [51] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2002). [52] S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77, 042303 (2008). [53] Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. 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- Online documentation scipy.optimize.basinhopping [54] C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
- C. E. López, G. Romero, F. Lastra, E. Solano, and J. C. Retamal, Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems, Phys. Rev. Lett. 101, 080503 (2008). [55] J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). J. Yu, J. C. Retamal, M. Sanz, E. Solano, and F. Albarrán-Arriagada, Superconducting circuit architecture for digital-analog quantum computing, EPJ Quantum Technology 9, 9 (2022). [56] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
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- A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraf, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
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