Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 161 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 34 tok/s Pro
GPT-5 High 24 tok/s Pro
GPT-4o 120 tok/s Pro
Kimi K2 142 tok/s Pro
GPT OSS 120B 433 tok/s Pro
Claude Sonnet 4.5 35 tok/s Pro
2000 character limit reached

Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements (2404.14374v3)

Published 22 Apr 2024 in quant-ph and cond-mat.stat-mech

Abstract: We study temporal entanglement in dual-unitary Clifford circuits with probabilistic measurements preserving spatial unitarity. We exactly characterize the temporal entanglement barrier in the measurement-free regime, exhibiting ballistic growth and decay and a volume-law peak. In the presence of measurements, we relate the temporal entanglement to the scrambling properties of the circuit. For "good scramblers" measurements do not qualitatively change the temporal entanglement profile but only result in a reduced entanglement velocity, whereas for "poor scramblers" the initial ballistic growth of temporal entanglement with bath size is modified to diffusive. This difference is understood through a mapping of the underlying operator dynamics to a biased and an unbiased persistent random walk respectively. In the latter case measurements additionally modify the ballistic decay to the perfect dephaser limit, with vanishing temporal entanglement, to an exponential decay, which we describe through a spatial transfer matrix method. This spatial dynamics is shown to be described by a non-Hermitian hopping model, exhibiting a PT-breaking transition at a critical measurement rate $p=1/2$. In all cases the peak value of the temporal entanglement barrier exhibits volume-law scaling for all measurement rates.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (59)
  1. B. Jobst, A. Smith, and F. Pollmann, Finite-depth scaling of infinite quantum circuits for quantum critical points, Phys. Rev. Research 4, 033118 (2022).
  2. B. Bertini, P. Kos, and T. Prosen, Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions, Phys. Rev. Lett. 123, 210601 (2019a).
  3. B. Bertini, P. Kos, and T. Prosen, Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos, Phys. Rev. X 9, 021033 (2019b).
  4. S. Gopalakrishnan and A. Lamacraft, Unitary circuits of finite depth and infinite width from quantum channels, Phys. Rev. B 100, 064309 (2019).
  5. I. Reid and B. Bertini, Entanglement barriers in dual-unitary circuits, Phys. Rev. B 104, 014301 (2021).
  6. B. Bertini, P. Kos, and T. Prosen, Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits, SciPost Phys. 8, 067 (2020).
  7. P. W. Claeys and A. Lamacraft, Maximum velocity quantum circuits, Phys. Rev. Research 2, 033032 (2020).
  8. P. W. Claeys and A. Lamacraft, Ergodic and Nonergodic Dual-Unitary Quantum Circuits with Arbitrary Local Hilbert Space Dimension, Phys. Rev. Lett. 126, 100603 (2021).
  9. A. Flack, B. Bertini, and T. Prosen, Statistics of the spectral form factor in the self-dual kicked Ising model, Phys. Rev. Research 2, 043403 (2020).
  10. Y. Li, X. Chen, and M. P. A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100, 134306 (2019).
  11. Y. Li, X. Chen, and M. P. A. Fisher, Quantum Zeno effect and the many-body entanglement transition, Phys. Rev. B 98, 205136 (2018).
  12. Y. Bao, S. Choi, and E. Altman, Theory of the phase transition in random unitary circuits with measurements, Phys. Rev. B 101, 104301 (2020).
  13. M. J. Gullans and D. A. Huse, Dynamical Purification Phase Transition Induced by Quantum Measurements, Phys. Rev. X 10, 041020 (2020).
  14. X. Cao, A. Tilloy, and A. De Luca, Entanglement in a fermion chain under continuous monitoring, SciPost Phys. 7, 024 (2019).
  15. O. Alberton, M. Buchhold, and S. Diehl, Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law, Phys. Rev. Lett. 126, 170602 (2021).
  16. O. Lunt and A. Pal, Measurement-induced entanglement transitions in many-body localized systems, Phys. Rev. Research 2, 043072 (2020).
  17. M. A. Cazalilla and J. B. Marston, Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of-Equilibrium Systems, Phys. Rev. Lett. 88, 256403 (2002).
  18. S. R. White and A. E. Feiguin, Real-Time Evolution Using the Density Matrix Renormalization Group, Phys. Rev. Lett. 93, 076401 (2004).
  19. F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems, Phys. Rev. Lett. 93, 207204 (2004).
  20. G. Vidal, Efficient Classical Simulation of Slightly Entangled Quantum Computations, Phys. Rev. Lett. 91, 147902 (2003).
  21. P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech: Theory Exp. 2005, P04010 (2005).
  22. T. J. Osborne, Efficient Approximation of the Dynamics of One-Dimensional Quantum Spin Systems, Phys. Rev. Lett. 97, 157202 (2006).
  23. R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys. 349, 117 (2014).
  24. A. Müller-Hermes, J. I. Cirac, and M. C. Bañuls, Tensor network techniques for the computation of dynamical observables in one-dimensional quantum spin systems, New J. Phys. 14, 075003 (2012).
  25. M. B. Hastings and R. Mahajan, Connecting entanglement in time and space: Improving the folding algorithm, Phys. Rev. A 91, 032306 (2015).
  26. R. P. Feynman and F. L. Vernon, The theory of a general quantum system interacting with a linear dissipative system, Ann. Physics 24, 118 (1963).
  27. A. Lerose, M. Sonner, and D. A. Abanin, Influence Matrix Approach to Many-Body Floquet Dynamics, Phys. Rev. X 11, 021040 (2021a).
  28. K. Klobas, B. Bertini, and L. Piroli, Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton, Phys. Rev. Lett. 126, 160602 (2021).
  29. A. Lerose, M. Sonner, and D. A. Abanin, Scaling of temporal entanglement in proximity to integrability, Phys. Rev. B 104, 035137 (2021b).
  30. J. Thoenniss, A. Lerose, and D. A. Abanin, Nonequilibrium quantum impurity problems via matrix-product states in the temporal domain, Phys. Rev. B 107, 195101 (2023b).
  31. A. Foligno, T. Zhou, and B. Bertini, Temporal Entanglement in Chaotic Quantum Circuits, Phys. Rev. X 13, 041008 (2023a).
  32. S. Carignano, C. R. Marimón, and L. Tagliacozzo, On temporal entropy and the complexity of computing the expectation value of local operators after a quench, arXiv:2307.11649  (2023).
  33. M. Sonner, A. Lerose, and D. A. Abanin, Influence functional of many-body systems: Temporal entanglement and matrix-product state representation, Ann. Physics 435, 168677 (2021).
  34. A. Lerose, M. Sonner, and D. A. Abanin, Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality, Phys. Rev. B 107, L060305 (2023).
  35. G. Vidal, Efficient Simulation of One-Dimensional Quantum Many-Body Systems, Phys. Rev. Lett. 93, 040502 (2004).
  36. G. M. Sommers, D. A. Huse, and M. J. Gullans, Crystalline Quantum Circuits, PRX Quantum 4, 030313 (2023).
  37. W. W. Ho and S. Choi, Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics, Phys. Rev. Lett. 128, 060601 (2022).
  38. H. Wilming and I. Roth, High-temperature thermalization implies the emergence of quantum state designs, arXiv:2202.01669  (2022).
  39. S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A 70, 052328 (2004).
  40. B. Bertini, P. Kos, and T. Prosen, Localised Dynamics in the Floquet Quantum East Model, arXiv:2306.12467  (2023a).
  41. X.-H. Yu, Z. Wang, and P. Kos, Hierarchical generalization of dual unitarity, arXiv:2307.03138  (2023).
  42. M. A. Rampp, S. A. Rather, and P. W. Claeys, The entanglement membrane in exactly solvable lattice models, arXiv:2312.12509  (2023).
  43. A. Foligno, P. Kos, and B. Bertini, Quantum information spreading in generalised dual-unitary circuits, arXiv:2312.02940  (2023b).
  44. M. Ippoliti and V. Khemani, Postselection-Free Entanglement Dynamics via Spacetime Duality, Phys. Rev. Lett. 126, 060501 (2021).
  45. T.-C. Lu and T. Grover, Spacetime duality between localization transitions and measurement-induced transitions, PRX Quantum 2, 040319 (2021).
  46. S. Garratt and J. Chalker, Local Pairing of Feynman Histories in Many-Body Floquet Models, Phys. Rev. X 11, 021051 (2021).
  47. P. Kos, B. Bertini, and T. Prosen, Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula, Phys. Rev. X 11, 011022 (2021).
  48. P. W. Claeys and A. Lamacraft, Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics, Quantum 6, 738 (2022).
  49. M. Ippoliti and W. W. Ho, Dynamical Purification and the Emergence of Quantum State Designs from the Projected Ensemble, PRX Quantum 4, 030322 (2023).
  50. P. W. Claeys, A. Lamacraft, and J. Vicary, From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics, arXiv:2302.07280  (2023).
  51. L. Fidkowski, J. Haah, and M. B. Hastings, How Dynamical Quantum Memories Forget, Quantum 5, 382 (2021).
  52. M. Kac, A Stochastic Model Related to the Telegrapher’s Equation, Rocky Mountain J. Math. 4, 497 (1974).
  53. H. C. Berg, E. coli in Motion (Springer Science & Business Media, 2004).
  54. C. M. Bender and S. Boettcher, Real Spectra in Non-Hermitian Hamiltonians Having pt Symmetry, Phys. Rev. Lett. 80, 5243 (1998).
  55. C. M. Bender, Making sense of non-Hermitian Hamiltonians, Rep. Progr. Phys. 70, 947 (2007).
  56. W. D. Heiss, The physics of exceptional points, J. Phys. Math. Theor. 45, 444016 (2012).
  57. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  58. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Modern Phys. 93, 015005 (2021).
  59. S. Yao and Z. Wang, Edge states and topological invariants of non-hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
Citations (2)

Summary

We haven't generated a summary for this paper yet.

Dice Question Streamline Icon: https://streamlinehq.com

Open Questions

We haven't generated a list of open questions mentioned in this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

This paper has been mentioned in 2 tweets and received 0 likes.

Upgrade to Pro to view all of the tweets about this paper: