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Topology of Discrete Quantum Feedback Control

Published 13 Mar 2024 in cond-mat.mes-hall and quant-ph | (2403.08406v3)

Abstract: A general framework for analyzing the topology of quantum channels of single-particle systems is developed to find a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We provide a symmetry classification of quantum channels by identifying ten symmetry classes of discrete quantum feedback control with projective measurements. We construct various types of topological feedback control by using topological Maxwell demons that achieve robust feedback-controlled chiral or helical transport against noise and decoherence. Topological feedback control thus offers a versatile tool for creating and controlling nonequilibrium topological phases in open quantum systems that are distinct from non-Hermitian and Lindbladian systems and should provide a guiding principle for topology-based design of quantum feedback control.

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References (62)
  1. R. Moessner and J. E. Moore, Topological Phases of Matter (Cambridge University Press, Cambridge, 2021).
  2. X.-G. Wen, Colloquium: Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89, 041004 (2017).
  3. G. Ma, M. Xiao, and C. T. Chan, Topological phases in acoustic and mechanical systems, Nat. Rev. Phys. 1, 281 (2019).
  4. H. Xue, Y. Yang, and B. Zhang, Topological acoustics, Nat. Rev. Mater. 7, 974 (2022).
  5. K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance, Phys. Rev. Lett. 45, 494 (1980).
  6. R. B. Laughlin, Quantized hall conductivity in two dimensions, Phys. Rev. B 23, 5632 (1981).
  7. M. Büttiker, Absence of backscattering in the quantum hall effect in multiprobe conductors, Phys. Rev. B 38, 9375 (1988).
  8. Y. Hatsugai, Chern number and edge states in the integer quantum hall effect, Phys. Rev. Lett. 71, 3697 (1993).
  9. C. L. Kane and E. J. Mele, Quantum spin hall effect in graphene, Phys. Rev. Lett. 95, 226801 (2005a).
  10. C. L. Kane and E. J. Mele, Z2subscript𝑍2{Z}_{2}italic_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT topological order and the quantum spin hall effect, Phys. Rev. Lett. 95, 146802 (2005b).
  11. B. A. Bernevig and S.-C. Zhang, Quantum spin hall effect, Phys. Rev. Lett. 96, 106802 (2006).
  12. C. Wu, B. A. Bernevig, and S.-C. Zhang, Helical liquid and the edge of quantum spin hall systems, Phys. Rev. Lett. 96, 106401 (2006).
  13. A. Kitaev, Periodic table for topological insulators and superconductors, AIP Conf. Proc. 1134, 22 (2009).
  14. D. J. Thouless, Quantization of particle transport, Phys. Rev. B 27, 6083 (1983).
  15. T. Oka and H. Aoki, Photovoltaic hall effect in graphene, Phys. Rev. B 79, 081406 (2009).
  16. N. H. Lindner, G. Refael, and V. Galitski, Floquet topological insulator in semiconductor quantum wells, Nat. Phys. 7, 490 (2011).
  17. F. Nathan and M. S. Rudner, Topological singularities and the general classification of floquet–bloch systems, New J.Phys. 17, 125014 (2015).
  18. R. Roy and F. Harper, Periodic table for floquet topological insulators, Phys. Rev. B 96, 155118 (2017).
  19. S. Higashikawa, M. Nakagawa, and M. Ueda, Floquet chiral magnetic effect, Phys. Rev. Lett. 123, 066403 (2019).
  20. T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annu. Rev. Condens. Matter Phys. 10, 387–408 (2019).
  21. M. S. Rudner and N. H. Lindner, Band structure engineering and non-equilibrium dynamics in floquet topological insulators, Nat. Rev. Phys. 2, 229 (2020).
  22. H. Zhou and J. Y. Lee, Periodic table for topological bands with non-hermitian symmetries, Phys. Rev. B 99, 235112 (2019).
  23. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  24. C.-H. Liu, H. Hu, and S. Chen, Symmetry and topological classification of floquet non-hermitian systems, Phys. Rev. B 105, 214305 (2022).
  25. N. Okuma and M. Sato, Non-hermitian topological phenomena: A review, Annu. Rev. Condens. Matter Phys. 14, 83 (2023).
  26. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2011).
  27. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
  28. J. C. Maxwell, Theory of Heat (Appleton, London, 1871).
  29. T. Sagawa and M. Ueda, Second law of thermodynamics with discrete quantum feedback control, Phys. Rev. Lett. 100, 080403 (2008).
  30. J. M. R. Parrondo, J. M. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  31. S. Lieu, M. McGinley, and N. R. Cooper, Tenfold way for quadratic lindbladians, Phys. Rev. Lett. 124, 040401 (2020).
  32. L. Sá, P. Ribeiro, and T. Prosen, Symmetry classification of many-body lindbladians: Tenfold way and beyond, Phys. Rev. X 13, 031019 (2023).
  33. Y. Ashida, Z. Gong, and M. Ueda, Non-hermitian physics, Adv. Phys. 69, 249 (2020).
  34. T. E. Lee, Anomalous edge state in a non-hermitian lattice, Phys. Rev. Lett. 116, 133903 (2016).
  35. S. Yao and Z. Wang, Edge states and topological invariants of non-hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
  36. K. Yokomizo and S. Murakami, Non-bloch band theory of non-hermitian systems, Phys. Rev. Lett. 123, 066404 (2019).
  37. K. Zhang, Z. Yang, and C. Fang, Correspondence between winding numbers and skin modes in non-hermitian systems, Phys. Rev. Lett. 125, 126402 (2020).
  38. D. Bernard and A. LeClair, A classification of non-hermitian random matrices, in Statistical Field Theories (Springer Netherlands, 2002) pp. 207–214.
  39. A. Rivas and S. F. Huelga, Open Quantum Systems (Springer Berlin Heidelberg, 2012).
  40. A. Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep. Math. Phys. 3, 275 (1972).
  41. M.-D. Choi, Completely positive linear maps on complex matrices, Linear Alg. Appl. 10, 285 (1975).
  42. M. Jiang, S. Luo, and S. Fu, Channel-state duality, Phys. Rev. A 87, 022310 (2013).
  43. M. M. Wilde, Quantum Information Theory (Cambridge University Press, Cambridge, 2013).
  44. A. Hatcher, Algebraic Topology (Cambridge University Press, Cambridge, 2001).
  45. K. Liu, M. Nakagawa, and M. Ueda, Maxwell’s demon for quantum transport, arXiv:2303.08326  (2023).
  46. T. Sagawa and M. Ueda, Generalized jarzynski equality under nonequilibrium feedback control, Phys. Rev. Lett. 104, 090602 (2010).
  47. N. Hatano and D. R. Nelson, Localization transitions in non-hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996).
  48. N. Hatano and D. R. Nelson, Vortex pinning and non-hermitian quantum mechanics, Phys. Rev. B 56, 8651 (1997).
  49. N. Hatano and D. R. Nelson, Non-hermitian delocalization and eigenfunctions, Phys. Rev. B 58, 8384 (1998).
  50. T. Mori and T. Shirai, Resolving a discrepancy between liouvillian gap and relaxation time in boundary-dissipated quantum many-body systems, Phys. Rev. Lett. 125, 230604 (2020).
  51. B. Buča and T. Prosen, A note on symmetry reductions of the lindblad equation: transport in constrained open spin chains, New J. Phys. 14, 073007 (2012).
  52. V. V. Albert and L. Jiang, Symmetries and conserved quantities in lindblad master equations, Phys. Rev. A 89, 022118 (2014).
  53. C. de Groot, A. Turzillo, and N. Schuch, Symmetry Protected Topological Order in Open Quantum Systems, Quantum 6, 856 (2022).
  54. A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997).
  55. M. Kawasaki, K. Mochizuki, and H. Obuse, Topological phases protected by shifted sublattice symmetry in dissipative quantum systems, Phys. Rev. B 106, 035408 (2022).
  56. H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007).
  57. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  58. K. Shiraishi et al., in preparation.
  59. A. J. Daley, Quantum trajectories and open many-body quantum systems, Adv. Phys. 63, 77 (2014).
  60. C. Gross and W. S. Bakr, Quantum gas microscopy for single atom and spin detection, Nat. Phys. 17, 1316–1323 (2021).
  61. A. Browaeys and T. Lahaye, Many-body physics with individually controlled rydberg atoms, Nat. Phys. 16, 132–142 (2020).
  62. Z. Gong, R. Hamazaki, and M. Ueda, Discrete time-crystalline order in cavity and circuit qed systems, Phys. Rev. Lett. 120, 040404 (2018b).

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