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  • Open Access

Measurement-Altered Ising Quantum Criticality

Sara Murciano, Pablo Sala, Yue Liu, Roger S. K. Mong, and Jason Alicea
Phys. Rev. X 13, 041042 – Published 5 December 2023
  1. Y. Li, X. Chen, and M. P. A. Fisher, Quantum Zeno effect and the many-body entanglement transition, Phys. Rev. B 98, 205136 (2018).
  2. B. Skinner, J. Ruhman, and A. Nahum, Measurement-induced phase transitions in the dynamics of entanglement, Phys. Rev. X 9, 031009 (2019).
  3. Y. Li, X. Chen, and M. P. A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100, 134306 (2019).
  4. A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, Unitary-projective entanglement dynamics, Phys. Rev. B 99, 224307 (2019).
  5. M. J. Gullans and D. A. Huse, Dynamical purification phase transition induced by quantum measurements, Phys. Rev. X 10, 041020 (2020).
  6. S. Choi, Y. Bao, X.-L. Qi, and E. Altman, Quantum error correction in scrambling dynamics and measurement-induced phase transition, Phys. Rev. Lett. 125, 030505 (2020).
  7. C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, Measurement-induced criticality in random quantum circuits, Phys. Rev. B 101, 104302 (2020).
  8. 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).
  9. A. Biella and M. Schiró, Many-body quantum Zeno effect and measurement-induced subradiance transition, Quantum 5, 528 (2021).
  10. X. Turkeshi, L. Piroli, and M. Schiró, Enhanced entanglement negativity in boundary-driven monitored fermionic chains, Phys. Rev. B 106, 024304 (2022).
  11. X. Cao, A. Tilloy, and A. D. Luca, Entanglement in a fermion chain under continuous monitoring, SciPost Phys. 7, 024 (2019).
  12. M. J. Gullans and D. A. Huse, Scalable probes of measurement-induced criticality, Phys. Rev. Lett. 125, 070606 (2020).
  13. Y. Bao, S. Choi, and E. Altman, Theory of the phase transition in random unitary circuits with measurements, Phys. Rev. B 101, 104301 (2020).
  14. T. Boorman, M. Szyniszewski, H. Schomerus, and A. Romito, Diagnostics of entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition, Phys. Rev. B 105, 144202 (2022).
  15. R. Fan, S. Vijay, A. Vishwanath, and Y.-Z. You, Self-organized error correction in random unitary circuits with measurement, Phys. Rev. B 103, 174309 (2021).
  16. G. S. Bentsen, S. Sahu, and B. Swingle, Measurement-induced purification in large-N hybrid Brownian circuits, Phys. Rev. B 104, 094304 (2021).
  17. Y. Li, X. Chen, A. W. W. Ludwig, and M. P. A. Fisher, Conformal invariance and quantum nonlocality in critical hybrid circuits, Phys. Rev. B 104, 104305 (2021).
  18. A. J. Friedman, C. Yin, Y. Hong, and A. Lucas, Locality and Error Correction in Quantum Dynamics with Measurement, Locality and error correction in quantum dynamics with measurement arXiv:2206.09929.
  19. X. Turkeshi, R. Fazio, and M. Dalmonte, Measurement-induced criticality in (2+1)-dimensional hybrid quantum circuits, Phys. Rev. B 102, 014315 (2020).
  20. X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and M. Schiró, Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks, Phys. Rev. B 103, 224210 (2021).
  21. T. Müller, S. Diehl, and M. Buchhold, Measurement-induced dark state phase transitions in long-ranged fermion systems, Phys. Rev. Lett. 128, 010605 (2022).
  22. A. Lavasani, A. Y., and M. Maissam Barkeshli, Measurement-induced topological entanglement transitions in symmetric random quantum circuits, Nat. Phys. 17, 342 (2021).
  23. S. Sang and T. H. Hsieh, Measurement-protected quantum phases, Phys. Rev. Res. 3, 023200 (2021).
  24. Y. Bao, S. Choi, and E. Altman, Symmetry enriched phases of quantum circuits, Ann. Phys. (Amsterdam) 435, 168618 (2021).
  25. M. Van Regemortel, Z.-P. Cian, A. Seif, H. Dehghani, and M. Hafezi, Entanglement entropy scaling transition under competing monitoring protocols, Phys. Rev. Lett. 126, 123604 (2021).
  26. M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, Entanglement phase transitions in measurement-only dynamics, Phys. Rev. X 11, 011030 (2021).
  27. X. Turkeshi, M. Dalmonte, R. Fazio, and M. Schirò, Entanglement transitions from stochastic resetting of non-Hermitian quasiparticles, Phys. Rev. B 105, L241114 (2022).
  28. X. Turkeshi and M. Schiró, Entanglement and correlation spreading in non-Hermitian spin chains, Phys. Rev. B 107, L020403 (2023).
  29. P. Sierant, G. Chiriacò, F. M. Surace, S. Sharma, X. Turkeshi, M. Dalmonte, R. Fazio, and G. Pagano, Dissipative Floquet dynamics: From steady state to measurement induced criticality in trapped-ion chains, Quantum 6, 638 (2022).
  30. M. Coppola, E. Tirrito, D. Karevski, and M. Collura, Growth of entanglement entropy under local projective measurements, Phys. Rev. B 105, 094303 (2022).
  31. S. P. Kelly, U. Poschinger, F. Schmidt-Kaler, M. P. A. Fisher, and J. Marino, Coherence Requirements for Quantum Communication from Hybrid Circuit Dynamics, Coherence requirements for quantum communication from hybrid circuit dynamics arXiv:2210.11547.
  32. L. Piroli, G. Styliaris, and J. I. Cirac, Quantum circuits assisted by local operations and classical communication: Transformations and phases of matter, Phys. Rev. Lett. 127, 220503 (2021).
  33. R. Verresen, N. Tantivasadakarn, and A. Vishwanath, Efficiently Preparing Schroedinger’s Cat, Fractons and Non-Abelian Topological Order in Quantum Devices, Efficiently preparing Schroedinger’s cat, fractons and non-Abelian topological order in quantum devices arXiv:2112.03061.
  34. N. Tantivasadakarn, R. Thorngren, A. Vishwanath, and R. Verresen, Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases, Long-range entanglement from measuring symmetry-protected topological phases arXiv:2112.01519.
  35. N. Tantivasadakarn, A. Vishwanath, and R. Verresen, Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward, PRX Quantum 4, 020339 (2023).
  36. T.-C. Lu, L. A. Lessa, I. H. Kim, and T. H. Hsieh, Measurement as a shortcut to long-range entangled quantum matter, PRX Quantum 3, 040337 (2022).
  37. S. Bravyi, I. Kim, A. Kliesch, and R. Koenig, Adaptive Constant-Depth Circuits for Manipulating Non-Abelian Anyons, Adaptive constant-depth circuits for manipulating non-Abelian anyons arXiv:2205.01933.
  38. G.-Y. Zhu, N. Tantivasadakarn, A. Vishwanath, S. Trebst, and R. Verresen, Nishimori’s Cat: Stable Long-Range Entanglement from Finite-Depth Unitaries and Weak Measurements, Nishimori’s cat: Stable long-range entanglement from finite-depth unitaries and weak measurements arXiv:2208.11136.
  39. J. Y. Lee, W. Ji, Z. Bi, and M. P. A. Fisher, Decoding Measurement-Prepared Quantum Phases and Transitions: From Ising Model to Gauge Theory, and Beyond, Decoding measurement-prepared quantum phases and transitions: From Ising model to gauge theory, and beyond arXiv:2208.11699.
  40. L. P. García-Pintos, D. Tielas, and A. del Campo, Spontaneous symmetry breaking induced by quantum monitoring, Phys. Rev. Lett. 123, 090403 (2019).
  41. C. Noel, P. Niroula, A. Zhu, Dand Risinger, L. Egan, D. Biswas, M. Cetina, A. V. Gorshkov, M. J. Gullans, D. A. Huse, and C. Monroe, Measurement-induced quantum phases realized in a trapped-ion quantum computer, Nat. Phys. 18, 760 (2022).
  42. J. M. Koh, S.-N. Sun, M. Motta, and A. J. Minnich, Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout, Nat. Phys. 19, 1314 (2023).
  43. M. Iqbal, N. Tantivasadakarn, T. M. Gatterman, J. A. Gerber, K. Gilmore, D. Gresh, A. Hankin, N. Hewitt, C. V. Horst, and M. Matheny et al., Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer, Topological order from measurements and feed-forward on a trapped ion quantum computer arXiv:2302.01917.
  44. Z. Weinstein, S. P. Kelly, J. Marino, and E. Altman, Scrambling Transition in a Radiative Random Unitary Circuit, Scrambling transition in a radiative random unitary circuit arXiv:2210.14242.
  45. H. Dehghani, A. Lavasani, M. Hafezi, and M. J. Gullans, Neural-network decoders for measurement induced phase transitions, Nat. Commun. 14, 2918 (2023).
  46. X. Turkeshi, Measurement-induced criticality as a data-structure transition, Phys. Rev. B 106, 144313 (2022).
  47. M. Ippoliti and V. Khemani, Postselection-free entanglement dynamics via spacetime duality, Phys. Rev. Lett. 126, 060501 (2021).
  48. M. Ippoliti, T. Rakovszky, and V. Khemani, Fractal, logarithmic, and volume-law entangled nonthermal steady states via spacetime duality, Phys. Rev. X 12, 011045 (2022).
  49. T.-C. Lu and T. Grover, Spacetime duality between localization transitions and measurement-induced transitions, PRX Quantum 2, 040319 (2021).
  50. Y. Li, Y. Zou, P. Glorioso, E. Altman, and M. P. A. Fisher, Cross entropy benchmark for measurement-induced phase transitions, Phys. Rev. Lett. 130, 220404 (2023).
  51. S. J. Garratt, Z. Weinstein, and E. Altman, Measurements conspire nonlocally to restructure critical quantum states, Phys. Rev. X 13, 021026 (2023).
  52. C. L. Kane and M. P. A. Fisher, Transport in a one-channel Luttinger liquid, Phys. Rev. Lett. 68, 1220 (1992).
  53. E. Tirrito, A. Santini, R. Fazio, and M. Collura, Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain, SciPost Phys. 15, 096 (2023).
  54. D. Rossini and E. Vicari, Measurement-induced dynamics of many-body systems at quantum criticality, Phys. Rev. B 102, 035119 (2020).
  55. C.-J. Lin, W. Ye, Y. Zou, S. Sang, and T. H. Hsieh, Probing sign structure using measurement-induced entanglement, Quantum 7, 910 (2023).
  56. X. Sun, H. Yao, and S.-K. Jian, New Critical States Induced by Measurement, New critical states induced by measurement arXiv:2301.11337.
  57. J. Y. Lee, C.-M. Jian, and C. Xu, Quantum criticality under decoherence or weak measurement, PRX Quantum 4, 030317 (2023).
  58. Y. Bao, R. Fan, A. Vishwanath, and E. Altman, Mixed-State Topological Order and the Errorfield Double Formulation of Decoherence-Induced Transitions, Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions arXiv:2301.05687.
  59. R. Fan, Y. Bao, E. Altman, and A. Vishwanath, Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory, Diagnostics of mixed-state topological order and breakdown of quantum memory arXiv:2301.05689.
  60. Y. Zou, S. Sang, and T. H. Hsieh, Channeling quantum criticality, Phys. Rev. Lett. 130, 250403 (2023).
  61. K. Slagle, D. Aasen, H. Pichler, R. S. K. Mong, P. Fendley, X. Chen, M. Endres, and J. Alicea, Microscopic characterization of Ising conformal field theory in Rydberg chains, Phys. Rev. B 104, 235109 (2021).
  62. P. Scholl, A. L. Shaw, R. B.-S. Tsai, R. Finkelstein, J. Choi, and M. Endres, Erasure Conversion in a High-Fidelity Rydberg Quantum Simulator, Erasure conversion in a high-fidelity Rydberg quantum simulator arXiv:2305.03406.
  63. R. Haghshenas, E. Chertkov, M. DeCross, T. M. Gatterman, J. A. Gerber, K. Gilmore, D. Gresh, N. Hewitt, C. V. Horst, and M. Matheny et al., Probing Critical States of Matter on a Digital Quantum Computer, Probing critical states of matter on a digital quantum computer arXiv:2305.01650.
  64. P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory (Springer-Verlag New York Inc., New York, 1997).
  65. Notice that iγRγL=0 when evaluated in the critical Ising CFT.
  66. Otherwise, the measurement translates into a control unitary on the top chain depending on the measurement outcome of the bottom chain.
  67. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th ed. (Cambridge University Press, Cambridge, England, 2011).
  68. J. Hauschild and F. Pollmann, Efficient numerical simulations with tensor networks: Tensor Network Python (tenpy), code available from SciPost Phys. Lect. Notes 5 (2018).
  69. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  70. I. P. McCulloch, Infinite Size Density Matrix Renormalization Group, Revisited, Infinite size density matrix renormalization group, revisited arXiv:0804.2509.
  71. S. Bravyi, D. P. Divincenzo, R. Oliveira, and B. M. Terhal, The complexity of stoquastic local Hamiltonian problems, Quantum Inf. Comput. 8, 361 (2008).
  72. The high probability of this measurement outcome becomes intuitive in the hanc/Janc1 regime.
  73. Explicitly, after dropping terms that vanish by time-reversal symmetry, one finds (U)ZjZjUs˜=cos[2ua(j)]cos[2ua(j)]ZjZjs˜+sin[2ua(j)]sin[2ua(j)]YjYjs˜. Given that (i) Yj maps to a CFT operator with larger scaling dimension than that for Zj (Yjiτσ, Δτσ=9/8 [74]) and (ii) our perturbative expansion focuses on the u1 regime, the U unitary can be safely neglected.
  74. P. Pfeuty, The one-dimensional Ising model with a transverse field, Ann. Phys. (N.Y.) 57, 79 (1970).
  75. B. M. McCoy and J. H. H. Perk, Spin correlation functions of an Ising model with continuous exponents, Phys. Rev. Lett. 44, 840 (1980).
  76. D. Cabra and C. Naó, 2D Ising model with a defect line, Mod. Phys. Lett. A 09, 2107 (1994).
  77. C. Naón and M. Trobo, The spin correlation function in 2D statistical mechanics models with inhomogeneous line defects, J. Stat. Mech. 2011, P02021.
  78. P. Sala, S. Murciano, Y. Liu, and J. Alicea (to be published).
  79. Notice that for C=0, |ψs˜ is an eigenstate of G, even though U breaks this symmetry explicitly.
  80. We show connected correlations, as for finite bond dimension Zs˜ gives nonzero values.
  81. T. Koffel, M. Lewenstein, and L. Tagliacozzo, Entanglement entropy for the long-range Ising chain in a transverse field, Phys. Rev. Lett. 109, 267203 (2012).
  82. D. Vodola, L. Lepori, E. Ercolessi, and G. Pupillo, Long-range Ising and Kitaev models: Phases, correlations and edge modes, New J. Phys. 18, 015001 (2015).
  83. Notice that targeting a particular outcome is different from characterizing typical outcomes, for which our field theory results might not apply.
  84. G. van Kempen and L. van Vliet, Mean and variance of ratio estimators used in fluorescence ratio imaging, Cytometry 39, 300 (2000).
  85. Equation (93) provides the leading N dependence needed to ensure that VarM[r(A)]/r(A) becomes smaller than 1 for the cases of interest. This conclusion follows from the fact that r(A) decays at most as a power law in system size, whereas the factor in braces in Eq. (92) is at most O(1).
  86. P. Fendley, K. Sengupta, and S. Sachdev, Competing density-wave orders in a one-dimensional hard-boson model, Phys. Rev. B 69, 075106 (2004).
  87. Z. Weinstein, R. Sajith, E. Altman, and S. J. Garratt, Nonlocality and entanglement in measured critical quantum Ising chains, Phys. Rev. B 107, 245132 (2023).
  88. Z. Yang, D. Mao, and C.-M. Jian, Entanglement in a one-dimensional critical state after measurements, Phys. Rev. B 108, 165120 (2023).
  89. J. I. Latorre, E. Rico, and G. Vidal, Ground state entanglement in quantum spin chains, Quantum Inf. Comput. 4, 48 (2004).
  90. J. Surace and L. Tagliacozzo, Fermionic Gaussian states: An introduction to numerical approaches, SciPost Phys. Lect. Notes 54 (2022).
  91. H. Widom, Asymptotic behavior of block Toeplitz matrices and determinants, Adv. Math. 13, 284 (1974).

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