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Measurement-Induced Landscape Transitions and Coding Barren Plateaus in Hybrid Variational Quantum Circuits (2312.09135v2)
Published 14 Dec 2023 in quant-ph, cond-mat.stat-mech, and cond-mat.str-el
Abstract: The entanglement-induced barren plateau is an exponential vanishing of the parameter gradients with system size that limits the practical application of variational quantum algorithms(VQA). A landscape transition from barren plateau to no-barren plateau was recently observed in monitored quantum circuits, hypothesized to coincide with the measurement-induced phase transition (MIPT) that separates the area-law states from the volume-law states. We argue from an information theory perspective that these are different transitions. This hypothesis is supported by a numerical study that includes cost-gradient variances, visualizations of the optimization runs and cost-landscape, and a quantum-classical channel mutual information measure. The results are evidence for a universal measurement-induced landscape transition (MILT) at $p_c{\text{MILT}} \approx 0.2 < p_c{\text{MIPT}}$ and that throughout $0<p<p_c{\text{MILT}}$, there is a finite quantum-classical channel mutual information in the limit of a large number of qubits. Unlike the barren plateau without measurements, a non-zero rate of measurements induces a coding barren plateau where, typically, information about the parameters is available to a local cost function despite a vanishing gradient.
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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, Y., Chen, X., Fisher, M.P.A.: Measurement-driven entanglement transition in hybrid quantum circuits. Phys. Rev. B 100, 134306 (2019) https://doi.org/10.1103/PhysRevB.100.134306 Skinner et al. [2019] Skinner, B., Ruhman, J., Nahum, A.: Measurement-induced phase transitions in the dynamics of entanglement. Phys. Rev. X 9, 031009 (2019) https://doi.org/10.1103/PhysRevX.9.031009 Preskill [2018] Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018) https://doi.org/10.22331/q-2018-08-06-79 Peruzzo et al. [2014] Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P.J., Aspuru-Guzik, A., O’Brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nature Communications 5(1), 4213 (2014) https://doi.org/10.1038/ncomms5213 McClean et al. [2016] McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New Journal of Physics 18(2), 023023 (2016) https://doi.org/10.1088/1367-2630/18/2/023023 Cerezo et al. [2021] Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., Coles, P.J.: Variational quantum algorithms. Nature Reviews Physics 3(9), 625–644 (2021) https://doi.org/10.1038/s42254-021-00348-9 Sim et al. [2019] Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Skinner, B., Ruhman, J., Nahum, A.: Measurement-induced phase transitions in the dynamics of entanglement. Phys. Rev. X 9, 031009 (2019) https://doi.org/10.1103/PhysRevX.9.031009 Preskill [2018] Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018) https://doi.org/10.22331/q-2018-08-06-79 Peruzzo et al. [2014] Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P.J., Aspuru-Guzik, A., O’Brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nature Communications 5(1), 4213 (2014) https://doi.org/10.1038/ncomms5213 McClean et al. [2016] McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New Journal of Physics 18(2), 023023 (2016) https://doi.org/10.1088/1367-2630/18/2/023023 Cerezo et al. [2021] Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., Coles, P.J.: Variational quantum algorithms. Nature Reviews Physics 3(9), 625–644 (2021) https://doi.org/10.1038/s42254-021-00348-9 Sim et al. [2019] Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. 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[2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New Journal of Physics 18(2), 023023 (2016) https://doi.org/10.1088/1367-2630/18/2/023023 Cerezo et al. [2021] Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., Coles, P.J.: Variational quantum algorithms. Nature Reviews Physics 3(9), 625–644 (2021) https://doi.org/10.1038/s42254-021-00348-9 Sim et al. [2019] Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., Coles, P.J.: Variational quantum algorithms. Nature Reviews Physics 3(9), 625–644 (2021) https://doi.org/10.1038/s42254-021-00348-9 Sim et al. [2019] Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. 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Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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New Journal of Physics 18(2), 023023 (2016) https://doi.org/10.1088/1367-2630/18/2/023023 Cerezo et al. [2021] Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., Coles, P.J.: Variational quantum algorithms. Nature Reviews Physics 3(9), 625–644 (2021) https://doi.org/10.1038/s42254-021-00348-9 Sim et al. [2019] Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018) https://doi.org/10.22331/q-2018-08-06-79 Peruzzo et al. [2014] Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P.J., Aspuru-Guzik, A., O’Brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nature Communications 5(1), 4213 (2014) https://doi.org/10.1038/ncomms5213 McClean et al. [2016] McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New Journal of Physics 18(2), 023023 (2016) https://doi.org/10.1088/1367-2630/18/2/023023 Cerezo et al. [2021] Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., Coles, P.J.: Variational quantum algorithms. Nature Reviews Physics 3(9), 625–644 (2021) https://doi.org/10.1038/s42254-021-00348-9 Sim et al. [2019] Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. 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[2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. 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[2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. 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[2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. 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[2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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[2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. 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[2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Sim, S., Johnson, P.D., Aspuru-Guzik, A.: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies 2(12), 1900070 (2019) https://doi.org/10.1002/qute.201900070 Haug et al. [2021] Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Haug, T., Bharti, K., Kim, M.S.: Capacity and quantum geometry of parametrized quantum circuits. PRX Quantum 2, 040309 (2021) https://doi.org/10.1103/PRXQuantum.2.040309 Holmes et al. [2022] Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum 3, 010313 (2022) https://doi.org/10.1103/PRXQuantum.3.010313 McClean et al. [2018] McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4 Cerezo et al. [2021] Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. 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[2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. 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[2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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- Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications 12(1), 1791 (2021) https://doi.org/10.1038/s41467-021-21728-w Wang et al. [2021] Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12(1), 6961 (2021) https://doi.org/10.1038/s41467-021-27045-6 Ortiz Marrero et al. [2021] Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. 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[2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Ortiz Marrero, C., Kieferová, M., Wiebe, N.: Entanglement-induced barren plateaus. PRX Quantum 2, 040316 (2021) https://doi.org/10.1103/PRXQuantum.2.040316 Mele et al. [2022] Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Mele, A.A., Mbeng, G.B., Santoro, G.E., Collura, M., Torta, P.: Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz. Phys. Rev. A 106, 060401 (2022) https://doi.org/10.1103/PhysRevA.106.L060401 Grimsley et al. [2023] Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Barron, G.S., Barnes, E., Economou, S.E., Mayhall, N.J.: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information 9(1), 19 (2023) Friedrich and Maziero [2022] Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. 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[2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Friedrich, L., Maziero, J.: Avoiding barren plateaus with classical deep neural networks. Phys. Rev. A 106, 042433 (2022) https://doi.org/10.1103/PhysRevA.106.042433 Grant et al. [2019] Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grant, E., Wossnig, L., Ostaszewski, M., Benedetti, M.: An initialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum 3, 214 (2019) https://doi.org/10.22331/q-2019-12-09-214 Patti et al. [2021] Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. 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[2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Patti, T.L., Najafi, K., Gao, X., Yelin, S.F.: Entanglement devised barren plateau mitigation. Phys. Rev. Res. 3, 033090 (2021) https://doi.org/10.1103/PhysRevResearch.3.033090 Sack et al. [2022] Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Sack, S.H., Medina, R.A., Michailidis, A.A., Kueng, R., Serbyn, M.: Avoiding barren plateaus using classical shadows. PRX Quantum 3, 020365 (2022) https://doi.org/10.1103/PRXQuantum.3.020365 Nahum et al. [2017] Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nahum, A., Ruhman, J., Vijay, S., Haah, J.: Quantum entanglement growth under random unitary dynamics. Phys. Rev. X 7, 031016 (2017) https://doi.org/10.1103/PhysRevX.7.031016 Jian et al. [2020] Jian, C.-M., You, Y.-Z., Vasseur, R., Ludwig, A.W.W.: Measurement-induced criticality in random quantum circuits. Phys. Rev. B 101, 104302 (2020) https://doi.org/10.1103/PhysRevB.101.104302 Lavasani et al. [2023] Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Lavasani, A., Luo, Z.-X., Vijay, S.: Monitored quantum dynamics and the kitaev spin liquid. Phys. Rev. B 108, 115135 (2023) https://doi.org/10.1103/PhysRevB.108.115135 Lavasani et al. [2021] Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Lavasani, A., Alavirad, Y., Barkeshli, M.: Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics 17(3), 342–347 (2021) https://doi.org/10.1038/s41567-020-01112-z Choi et al. [2020] Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Choi, S., Bao, Y., Qi, X.-L., Altman, E.: Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020) https://doi.org/10.1103/PhysRevLett.125.030505 Gullans and Huse [2020] Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. 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[2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. 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Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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[2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gullans, M.J., Huse, D.A.: Dynamical purification phase transition induced by quantum measurements. Phys. Rev. X 10, 041020 (2020) https://doi.org/10.1103/PhysRevX.10.041020 Holevo [2019] Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Holevo, A.S.: Quantum Systems, Channels, Information: a Mathematical Introduction. Walter de Gruyter GmbH and Co KG, ??? (2019) Kandala et al. [2017] Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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[2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879 Farhi et al. [2014] Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014) Wecker et al. [2015] Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. 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[2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. 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Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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[2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303 (2015) https://doi.org/10.1103/PhysRevA.92.042303 Kattemölle and van Wezel [2022] Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. 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[2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Kattemölle, J., Wezel, J.: Variational quantum eigensolver for the heisenberg antiferromagnet on the kagome lattice. Phys. Rev. B 106, 214429 (2022) https://doi.org/10.1103/PhysRevB.106.214429 Cong et al. [2019] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15(12), 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8 Pesah et al. [2021] Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Pesah, A., Cerezo, M., Wang, S., Volkoff, T., Sornborger, A.T., Coles, P.J.: Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X 11, 041011 (2021) https://doi.org/10.1103/PhysRevX.11.041011 Grimsley et al. [2019] Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. 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[2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications 10(1), 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2 Gyawali and Lawler [2022] Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Gyawali, G., Lawler, M.J.: Adaptive variational preparation of the fermi-hubbard eigenstates. Phys. Rev. A 105, 012413 (2022) https://doi.org/10.1103/PhysRevA.105.012413 Li et al. [2018] Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. 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[2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
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[2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. 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Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Li, H., Xu, Z., Taylor, G., Studer, C., Goldstein, T.: Visualizing the loss landscape of neural nets. Advances in neural information processing systems 31 (2018) Zabalo et al. [2020] Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. 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Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Zabalo, A., Gullans, M.J., Wilson, J.H., Gopalakrishnan, S., Huse, D.A., Pixley, J.H.: Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B 101, 060301 (2020) https://doi.org/10.1103/PhysRevB.101.060301 Paszke et al. [2019] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc. (2019). https://pytorch.org/docs/stable/index.html# Virtanen et al. [2020] Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020) https://doi.org/10.1038/s41592-019-0686-2 Efron and Tibshirani [1993] Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall/CRC, Boca Raton, Florida, USA (1993) Mitarai et al. [2018] Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Physical Review A 98(3) (2018) https://doi.org/10.1103/physreva.98.032309 Nocedal and Wright [1999] Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999) Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)
- Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, ??? (1999)