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Mpemba effects in quantum complexity

Sreemayee Aditya1,*, Alessandro Summer2,3, Piotr Sierant4, and Xhek Turkeshi1

  • *Contact author: asreemay@uni-koeln.de
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Phys. Rev. B 114, 074310 – Published 25 August, 2026

DOI: https://doi.org/10.1103/tyw6-pjp6

Abstract

The Mpemba effect, a system farther from equilibrium relaxing faster, has been demonstrated for thermodynamic and symmetry-based quantities in classical, open-quantum, and isolated many-body systems. Whether the same phenomenology extends to quantum resources connected to computational complexity remains unexplored. Here, we investigate the relaxation of coherence, imaginarity, fermionic non-Gaussianity, and magic in subsystems of closed quantum systems evolved under random circuits composed of free gates. We find that coherence and imaginarity display the quantum Mpemba effect (QME) for tilted product states, while non-Gaussianity and magic do not. All four resources exhibit the quantum Pontus-Mpemba effect: a resourceful preheating stage accelerates the subsequent free relaxation. A spectral analysis reveals that the QME is controlled by the overlap of the initial state with the slowest decay mode of the effective Liouvillian, and that generic preheating suppresses this overlap. These results demonstrate that Mpemba physics is not restricted to thermodynamic or symmetry observables, but constitutes a general feature of quantum resource dissipation in complexity-relevant settings.

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References (164)

  1. E. B. Mpemba and D. G. Osborne, Cool? Phys. Educ. 4, 172 (1969).
  2. G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja, Speedups in nonequilibrium thermal relaxation: Mpemba and related effects, Phys. Rep. 1164, 1 (2026).
  3. A. Lasanta, F. Vega Reyes, A. Prados, and A. Santos, When the hotter cools more quickly: Mpemba effect in granular fluids, Phys. Rev. Lett. 119, 148001 (2017).
  4. Z. Lu and O. Raz, Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse, Proc. Natl. Acad. Sci. USA 114, 5083 (2017).
  5. I. Klich, O. Raz, O. Hirschberg, and M. Vucelja, Mpemba index and anomalous relaxation, Phys. Rev. X 9, 021060 (2019).
  6. A. Kumar and J. Bechhoefer, Exponentially faster cooling in a colloidal system, Nature (London) 584, 64 (2020).
  7. J. Bechhoefer, A. Kumar, and R. Chétrite, A fresh understanding of the Mpemba effect, Nat. Rev. Phys. 3, 534 (2021).
  8. A. Kumar, R. Chétrite, and J. Bechhoefer, Anomalous heating in a colloidal system, Proc. Natl. Acad. Sci. USA 119, e2118484119 (2022).
  9. A. Nava and M. Fabrizio, Lindblad dissipative dynamics in the presence of phase coexistence, Phys. Rev. B 100, 125102 (2019).
  10. A. K. Chatterjee, S. Takada, and H. Hayakawa, Multiple quantum Mpemba effect: Exceptional points and oscillations, Phys. Rev. A 110, 022213 (2024).
  11. A. K. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba effect in a quantum dot with reservoirs, Phys. Rev. Lett. 131, 080402 (2023).
  12. S. Kochsiek, F. Carollo, and I. Lesanovsky, Accelerating the approach of dissipative quantum spin systems towards stationarity through global spin rotations, Phys. Rev. A 106, 012207 (2022).
  13. F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect, Phys. Rev. Lett. 127, 060401 (2021).
  14. F. Ivander, N. Anto-Sztrikacs, and D. Segal, Hyperacceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment, Phys. Rev. E 108, 014130 (2023).
  15. S. A. Shapira, Y. Shapira, J. Markov, G. Teza, N. Akerman, O. Raz, and R. Ozeri, Inverse Mpemba effect demonstrated on a single trapped ion qubit, Phys. Rev. Lett. 133, 010403 (2024).
  16. D. J. Strachan, A. Purkayastha, and S. R. Clark, Non-Markovian quantum Mpemba effect, Phys. Rev. Lett. 134, 220403 (2025).
  17. J. Zhang, G. Xia, C.-W. Wu, T. Chen, Q. Zhang, Y. Xie, W.-B. Su, W. Wu, C.-W. Qiu, P.-X. Chen, W. Li, H. Jing, and Y.-L. Zhou, Observation of quantum strong Mpemba effect, Nat. Commun. 16, 301 (2025).
  18. X. Wang and J. Wang, Mpemba effects in nonequilibrium open quantum systems, Phys. Rev. Res. 6, 033330 (2024).
  19. M. Moroder, O. Culhane, K. Zawadzki, and J. Goold, Thermodynamics of the quantum Mpemba effect, Phys. Rev. Lett. 133, 140404 (2024).
  20. P. Westhoff, S. Paeckel, and M. Moroder, Fast and direct preparation of a genuine lattice Bose-Einstein condensate via the quantum Mpemba effect, Phys. Rev. A 112, L061304 (2025).
  21. A. Nava and R. Egger, Pontus-Mpemba effects, Phys. Rev. Lett. 135, 140404 (2025).
  22. F. Ares, S. Murciano, and P. Calabrese, Entanglement asymmetry as a probe of symmetry breaking, Nat. Commun. 14, 2036 (2023).
  23. L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, and M. K. Joshi, Observing the quantum Mpemba effect in quantum simulations, Phys. Rev. Lett. 133, 010402 (2024).
  24. F. Ares, S. Murciano, E. Vernier, and P. Calabrese, Lack of symmetry restoration after a quantum quench: An entanglement asymmetry study, SciPost Phys. 15, 089 (2023).
  25. F. Ferro, F. Ares, and P. Calabrese, Non-equilibrium entanglement asymmetry for discrete groups: The example of the XY spin chain, J. Stat. Mech. (2024) 023101.
  26. S. Yamashika, F. Ares, and P. Calabrese, Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems, Phys. Rev. B 110, 085126 (2024).
  27. K. Chalas, F. Ares, C. Rylands, and P. Calabrese, Multiple crossings during dynamical symmetry restoration and implications for the quantum Mpemba effect, J. Stat. Mech. (2024) 103101.
  28. B. Bertini, K. Klobas, M. Collura, P. Calabrese, and C. Rylands, Dynamics of charge fluctuations from asymmetric initial states, Phys. Rev. B 109, 184312 (2024).
  29. X. Turkeshi, P. Calabrese, and A. De Luca, Quantum Mpemba effect in random circuits, Phys. Rev. Lett. 135, 040403 (2025).
  30. S. Liu, H.-K. Zhang, S. Yin, and S.-X. Zhang, Symmetry restoration and quantum Mpemba effect in symmetric random circuits, Phys. Rev. Lett. 133, 140405 (2024).
  31. S. Liu, H.-K. Zhang, S. Yin, S.-X. Zhang, and H. Yao, Symmetry restoration and quantum Mpemba effect in many-body localization systems, Sci. Bull. 70, 3991 (2025).
  32. F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba effects, Nat. Rev. Phys. 7, 451 (2025).
  33. F. Ares, C. Rylands, and P. Calabrese, A simpler probe of the quantum Mpemba effect in closed systems, J. Phys. A: Math. Theor. 58, 445302 (2025).
  34. T. Bhore, L. Su, I. Martin, A. A. Clerk, and Z. Papić, Quantum Mpemba effect without global symmetries, Phys. Rev. B 112, L121109 (2025).
  35. E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
  36. A. E. Deneris, P. Braccia, P. Bermejo, N. L. Diaz, A. A. Mele, and M. Cerezo, Analyzing the free states of one quantum resource theory as resource states of another, Adv. Quantum Technol. 9, e00702 (2026).
  37. N. L. Diaz, A. A. Mele, P. Bermejo, P. Braccia, A. E. Deneris, M. Larocca, and M. Cerezo, A unified approach to quantum resource theories and a new class of free operations, arXiv:2507.10851.
  38. A. Summer, M. Moroder, L. P. Bettmann, X. Turkeshi, I. Marvian, and J. Goold, Resource-theoretical unification of Mpemba effects: Classical and quantum, Phys. Rev. X 16, 011065 (2026).
  39. S. Aditya, X. Turkeshi, and P. Sierant, Growth and spreading of quantum resources under random circuit dynamics, Phys. Rev. Res. 8, 033062 (2026).
  40. G. C. Santra, A. Windey, S. Bandyopadhyay, A. Legramandi, and P. Hauke, Complexity transitions in chaotic quantum systems: Nonstabilizerness, entanglement, and fractal dimension in SYK and random matrix models, arXiv:2505.09707.
  41. G. C. Santra, J. Mildenberger, E. Ballini, A. Bottarelli, M. M. Wauters, and P. Hauke, Quantum resources in non-Abelian lattice gauge theories: Nonstabilizerness, multipartite entanglement, and fermionic non-Gaussianity, arXiv:2510.07385.
  42. N. D. Varikuti, S. Bandyopadhyay, and P. Hauke, Deep thermalization and measurements of quantum resources, arXiv:2512.09999.
  43. T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113, 140401 (2014).
  44. A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quantum coherence as a resource, Rev. Mod. Phys. 89, 041003 (2017).
  45. G. Saxena, E. Chitambar, and G. Gour, Dynamical resource theory of quantum coherence, Phys. Rev. Res. 2, 023298 (2020).
  46. S. Aditya, E. Tirrito, P. Sierant, and X. Turkeshi, Coherence dynamics in quantum many-body systems with conservation laws, arXiv:2604.23192.
  47. A. Sauliere, B. Magni, G. Lami, X. Turkeshi, and J. De Nardis, Universality in the anticoncentration of chaotic quantum circuits, Phys. Rev. B 112, 134312 (2025).
  48. G. Lami, J. De Nardis, and X. Turkeshi, Anticoncentration and state design of random tensor networks, Phys. Rev. Lett. 134, 010401 (2025).
  49. G. Lami, A. D. Luca, X. Turkeshi, and J. D. Nardis, Quantum state design and emergent confinement mechanism in measured tensor network states, arXiv:2504.16995.
  50. Y. Liu, P. Sierant, P. Stornati, M. Lewenstein, and M. Płodzień, Quantum algorithms for inverse participation ratio estimation in multiqubit and multiqudit systems, Phys. Rev. A 111, 052614 (2025).
  51. P. Sierant and X. Turkeshi, Universal behavior beyond multifractality of wave functions at measurement-induced phase transitions, Phys. Rev. Lett. 128, 130605 (2022).
  52. N. Macé, F. Alet, and N. Laflorencie, Multifractal scalings across the many-body localization transition, Phys. Rev. Lett. 123, 180601 (2019).
  53. D. J. Luitz, F. Alet, and N. Laflorencie, Universal behavior beyond multifractality in quantum many-body systems, Phys. Rev. Lett. 112, 057203 (2014).
  54. C. Liu, M. Ippoliti, and W. W. Ho, Coherence-induced deep thermalization transition in random permutation quantum dynamics, Phys. Rev. Lett. 136, 100404 (2026).
  55. Z. Cheng, E. Huang, V. Khemani, M. J. Gullans, and M. Ippoliti, Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements, PRX Quantum 6, 030333 (2025).
  56. S. P. Kelly, U. Poschinger, F. Schmidt-Kaler, M. P. A. Fisher, and J. Marino, Coherence requirements for quantum communication from hybrid circuit dynamics, SciPost Phys. 15, 250 (2023).
  57. X. Chen and Q. Lei, Imaginarity measures induced by relative entropy, Rep. Math. Phys. 95, 1 (2025).
  58. J. Xu, Quantifying the imaginarity of quantum states via Tsallis relative entropy, Phys. Lett. A 528, 130024 (2024).
  59. Y. Sun, R. Ren, Y. Wang, and Y. Li, Analysis of the relationship between imaginarity and entanglement, Phys. Rev. A 111, 032425 (2025).
  60. C. Wu and Z. Wu, Two imaginarity monotones induced by unified (α,β)-relative entropy, Commun. Theor. Phys. 77, 095101 (2025).
  61. B. Magni, M. Heinrich, L. Leone, and X. Turkeshi, Anticoncentration and state design of doped real Clifford circuits and tensor networks Phys. Rev. A 113, 062446 (2026).
  62. L. Lumia, E. Tirrito, R. Fazio, and M. Collura, Measurement-induced transitions beyond Gaussianity: A single particle description, Phys. Rev. Res. 6, 023176 (2024).
  63. M. Hebenstreit, R. Jozsa, B. Kraus, S. Strelchuk, and M. Yoganathan, All pure fermionic non-Gaussian states are magic states for matchgate computations, Phys. Rev. Lett. 123, 080503 (2019).
  64. X. Lyu and K. Bu, Displaced fermionic Gaussian states and their classical simulation, J. Phys. A Math. Theor. 58, 295301 (2025).
  65. P. Sierant, P. Stornati, and X. Turkeshi, Fermionic magic resources of quantum many-body systems, PRX Quantum 7, 010302 (2026).
  66. T. Haug, X. Turkeshi, and P. Sierant, Practical tests and witnesses of fermionic non-Gaussianity, arXiv:2605.26218.
  67. A. Paviglianiti, L. Lumia, E. Tirrito, A. Silva, M. Collura, X. Turkeshi, and G. Lami, Emergence of generic entanglement structure in doped matchgate circuits, Phys. Rev. Lett. 136, 020403 (2026).
  68. F. Ares, S. Murciano, and P. Calabrese, Non-Gaussianity of random quantum states, arXiv:2605.18986.
  69. S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
  70. S. Bravyi, G. Smith, and J. A. Smolin, Trading classical and quantum computational resources, Phys. Rev. X 6, 021043 (2016).
  71. Z.-W. Liu and A. Winter, Many-body quantum magic, PRX Quantum 3, 020333 (2022).
  72. D. Iannotti, B. Magni, R. Cioli, A. Hamma, and X. Turkeshi, Non-local magic resources for fermionic Gaussian states, arXiv:2604.27049.
  73. L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer Rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
  74. E. Tirrito, X. Turkeshi, and P. Sierant, Anticoncentration and nonstabilizerness spreading under ergodic quantum dynamics, Phys. Rev. Lett. 135, 220401 (2025).
  75. E. Tirrito, P. S. Tarabunga, D. S. Bhakuni, M. Dalmonte, P. Sierant, and X. Turkeshi, Universal spreading of nonstabilizerness and quantum transport, arXiv:2506.12133.
  76. B. Magni and X. Turkeshi, Quantum Complexity and chaos in many-qudit doped Clifford circuits, Quantum 9, 1956 (2025).
  77. X. Turkeshi, A. Dymarsky, and P. Sierant, Pauli spectrum and nonstabilizerness of typical quantum many-body states, Phys. Rev. B 111, 054301 (2025).
  78. B. Magni, A. Christopoulos, A. De Luca, and X. Turkeshi, Anticoncentration in Clifford circuits and beyond: From random tensor networks to pseudomagic states, Phys. Rev. X 15, 031071 (2025).
  79. P. R. N. Falcão, P. S. Tarabunga, M. Frau, E. Tirrito, J. Zakrzewski, and M. Dalmonte, Nonstabilizerness in U(1) lattice gauge theory, Phys. Rev. B 111, L081102 (2025).
  80. T. Haug, L. Aolita, and M. Kim, Probing quantum complexity via universal saturation of stabilizer entropies, Quantum 9, 1801 (2025).
  81. X. Qian, J. Huang, and M. Qin, Clifford circuits augmented time-dependent variational principle, Phys. Rev. Lett. 134, 150404 (2025).
  82. X. Qian, J. Huang, and M. Qin, Augmenting density matrix renormalization group with Clifford circuits, Phys. Rev. Lett. 133, 190402 (2024).
  83. T. Haug and P. S. Tarabunga, Efficient witnessing and testing of magic in mixed quantum states, npj Quantum Inf. 12, 40 (2026).
  84. G. Lami and M. Collura, Nonstabilizerness via perfect Pauli sampling of matrix product states, Phys. Rev. Lett. 131, 180401 (2023).
  85. G. Lami, T. Haug, and J. De Nardis, Quantum state designs with Clifford-enhanced matrix product states, PRX Quantum 6, 010345 (2025).
  86. A. Paviglianiti, G. Lami, M. Collura, and A. Silva, Estimating nonstabilizerness dynamics without simulating it, PRX Quantum 6, 030320 (2025).
  87. D. Sticlet, B. Dóra, D. Szombathy, G. Zaránd, and C. P. Moca, Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics, Phys. Rev. Res. 7, 043130 (2025).
  88. D. Szombathy, A. Valli, C. P. Moca, L. Farkas, and G. Zaránd, Asymptotically independent fluctuations of stabilizer Rényi entropy and entanglement in random unitary circuits, Phys. Rev. Res. 7, 043072 (2025).
  89. D. Szombathy, A. Valli, C. P. Moca, J. Asbóth, L. Farkas, T. Rakovszky, and G. Zaránd, Spectral properties versus magic generation in t-doped random Clifford circuits, Phys. Rev. Res. 7, 043080 (2025).
  90. J. Odavić, M. Viscardi, and A. Hamma, Stabilizer entropy in nonintegrable quantum evolutions, Phys. Rev. B 112, 104301 (2025).
  91. C. J. Cao, G. Cheng, A. Hamma, L. Leone, W. Munizzi, and S. F. E. Oliviero, Gravitational backreaction is magical, PRX Quantum 6, 040375 (2025).
  92. P. S. Tarabunga, E. Tirrito, T. Chanda, and M. Dalmonte, Many-body magic via Pauli-Markov chains—from criticality to gauge theories, PRX Quantum 4, 040317 (2023).
  93. D. Iannotti, A. Russotto, B. Jasser, J. Odavić, and A. Hamma, Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems, arXiv:2603.28870.
  94. Z.-Y. Hou, C. Cao, and Z.-C. Yang, Stabilizer entanglement enhances magic injection npj Quantum Inf. 12, 113 (2025).
  95. M. Bejan, C. McLauchlan, and B. Béri, Dynamical magic transitions in monitored Clifford+T circuits, PRX Quantum 5, 030332 (2024).
  96. E. Tirrito, L. Lumia, A. Paviglianiti, G. Lami, A. Silva, X. Turkeshi, and M. Collura, Magic phase transitions in monitored Gaussian fermions, arXiv:2507.07179.
  97. N. Dowling, P. Kos, and X. Turkeshi, Magic resources of the Heisenberg picture, Phys. Rev. Lett. 135, 050401 (2025).
  98. P. Niroula, C. D. White, Q. Wang, S. Johri, D. Zhu, C. Monroe, C. Noel, and M. J. Gullans, Phase transition in magic with random quantum circuits, Nat. Phys. 20, 1786 (2024).
  99. G. E. Fux, E. Tirrito, M. Dalmonte, and R. Fazio, Entanglement – nonstabilizerness separation in hybrid quantum circuits, Phys. Rev. Res. 6, L042030 (2024).
  100. P. R. N. Falcão, P. Sierant, J. Zakrzewski, and E. Tirrito, Nonstabilizerness dynamics in many-body localized systems, Phys. Rev. Lett. 135, 240404 (2025).
  101. P. Sierant and X. Turkeshi, Theory of magic phase transitions in encoding-decoding circuits, arXiv:2603.00235.
  102. X. Turkeshi, Coherent errors make magic, Nat. Phys. 20, 1696 (2024).
  103. N. Sun and P. Zhang, Connecting magic dynamics in thermofield double states to spectral form factors Phys. Rev. Lett. 137, 030401 (2026).
  104. M. Hoshino, M. Oshikawa, and Y. Ashida, Stabilizer Rényi entropy and conformal field theory, Phys. Rev. X 16, 011037 (2026).
  105. P. Zhang, S. Zhou, and N. Sun, Stabilizer Rényi entropy and its transition in the coupled Sachdev-Ye-Kitaev model, Phys. Rev. Lett. 136, 080201 (2026).
  106. N. Dowling, K. Modi, and G. A. L. White, Bridging entanglement and magic resources within operator space, Phys. Rev. Lett. 135, 160201 (2025).
  107. A. C. Nakhl, B. Harper, M. West, N. Dowling, M. Sevior, T. Quella, and M. Usman, Stabilizer tensor networks with magic state injection, Phys. Rev. Lett. 134, 190602 (2025).
  108. Z. Liu and B. K. Clark, Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states, Phys. Rev. Res. 8, 023116 (2026).
  109. H. Lóio, G. Lami, L. Leone, M. McGinley, X. Turkeshi, and J. D. Nardis, Quantum state designs via magic teleportation, arXiv:2510.13950.
  110. C. Vairogs and B. Yan, Extracting randomness from magic quantum states, Phys. Rev. Res. 7, L022069 (2025).
  111. A. Scocco, W.-K. Mok, L. Aolita, M. Collura, and T. Haug, Rise and fall of nonstabilizerness via random measurements, Phys. Rev. Res. 8, 013217 (2026).
  112. Y. Zhang and Y. Gu, Quantum magic dynamics in random circuits, npj Quantum Inf. 12, 87 (2024).
  113. S. Maity and R. Hamazaki, Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit, Phys. Rev. Res. 8, 013324 (2026).
  114. M. Bejan, P. W. Claeys, and J. Yao, Magic spreading under unitary Clifford dynamics, arXiv:2511.21487.
  115. E. Dallas and P. Zanardi, Nonlocal nonstabilizerness generation and information scrambling in noisy Clifford circuits, Phys. Rev. A 113, 042429 (2026).
  116. P. S. Tarabunga and E. Tirrito, Magic transition in measurement-only circuits, npj Quantum Inf. 11, 166 (2025).
  117. C. Wang, Z.-C. Yang, T. Zhou, and X. Chen, Magic transition in monitored free fermion dynamics, arXiv:2507.10688.
  118. L. Leone and L. Bittel, Stabilizer entropies are monotones for magic-state resource theory, Phys. Rev. A 110, L040403 (2024).
  119. S. Cusumano, L. C. Venuti, S. Cepollaro, G. Esposito, D. Iannotti, B. Jasser, J. Odavić, M. Viscardi, and A. Hamma, Non-stabilizerness and violations of CHSH inequalities, arXiv:2504.03351.
  120. L. Bittel and L. Leone, Operational interpretation of the stabilizer entropy, Quantum 10, 2069 (2026).
  121. T. Haug and L. Piroli, Stabilizer entropies and nonstabilizerness monotones, Quantum 7, 1092 (2023).
  122. Z. Xiao and S. Ryu, Exponentially accelerated sampling of Pauli strings for nonstabilizerness, arXiv:2601.00761.
  123. X. Huang, H.-Z. Li, C. H. Lee, and J.-X. Zhong, A fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm, arXiv:2512.24685.
  124. P. Sierant, J. Vallès-Muns, and A. Garcia-Saez, Computing quantum magic of state vectors, Quantum 10, 2059 (2026).
  125. P. Rall, D. Liang, J. Cook, and W. Kretschmer, Simulation of qubit quantum circuits via Pauli propagation, Phys. Rev. A 99, 062337 (2019).
  126. M. S. Rudolph, T. Jones, Y. Teng, A. Angrisani, and Z. Holmes, Pauli propagation: A computational framework for simulating quantum systems, arXiv:2505.21606.
  127. P. S. Tarabunga, E. Tirrito, M. C. Bañuls, and M. Dalmonte, Nonstabilizerness via matrix product states in the Pauli basis, Phys. Rev. Lett. 133, 010601 (2024).
  128. G. Lami and M. Collura, Unveiling the stabilizer group of a matrix product state, Phys. Rev. Lett. 133, 010602 (2024).
  129. X. Turkeshi, M. Schirò, and P. Sierant, Measuring nonstabilizerness via multifractal flatness, Phys. Rev. A 108, 042408 (2023).
  130. T. Haug and L. Piroli, Quantifying nonstabilizerness of matrix product states, Phys. Rev. B 107, 035148 (2023).
  131. J. Huang, X. Qian, and M. Qin, Clifford circuits augmented matrix product states for fermion systems, Phys. Rev. B 112, 205106 (2025).
  132. X. Qian, J. Huang, and M. Qin, Augmenting a finite-temperature tensor network with Clifford circuits, Phys. Rev. B 112, 115150 (2025).
  133. D. A. Korbany, M. J. Gullans, and L. Piroli, Long-range nonstabilizerness and phases of matter, Phys. Rev. Lett. 135, 160404 (2025).
  134. D. Qian and J. Wang, Quantum nonlocal nonstabilizerness, Phys. Rev. A 111, 052443 (2025).
  135. J. Huang, X. Qian, and M. Qin, Nonstabilizerness entanglement entropy: A measure of hardness in the classical simulation of quantum many-body systems with tensor network states, Phys. Rev. A 112, 012425 (2025).
  136. E. Tirrito, P. S. Tarabunga, G. Lami, T. Chanda, L. Leone, S. F. E. Oliviero, M. Dalmonte, M. Collura, and A. Hamma, Quantifying nonstabilizerness through entanglement spectrum flatness, Phys. Rev. A 109, L040401 (2024).
  137. F. B. Trigueros and J. A. M. Guzmán, Nonstabilizerness and error resilience in noisy quantum circuits Phys. Rev. Lett. 136, 240602 (2026).
  138. C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Murciano, and B. Bertini, Microscopic origin of the quantum Mpemba effect in integrable systems, Phys. Rev. Lett. 133, 010401 (2024).
  139. A. Nava, R. Egger, B. Dey, and D. Giuliano, Speeding up Pontus-Mpemba effects via dynamical phase transitions, Phys. Rev. Res. 7, 043332 (2025).
  140. X. Shi, Erasing imaginarity: An operational method, Phys. Rev. A 111, L050401 (2025).
  141. M. Howard and E. T. Campbell, Application of a resource theory for magic states to fault-tolerant quantum computing, Phys. Rev. Lett. 118, 090501 (2017).
  142. H. Hamaguchi, K. Hamada, and N. Yoshioka, Handbook for quantifying robustness of magic, Quantum 8, 1461 (2024).
  143. V. Veitch, C. Ferrie, D. Gross, and J. Emerson, Negative quasi-probability as a resource for quantum computation, New J. Phys. 14, 113011 (2012).
  144. X,Z denote Pauli matrices for d=2 and generalized Pauli operators for d>2 via Y=−iZX.
  145. P. R. N. Falcão, J. Zakrzewski, and P. Sierant, Fermionic magic resources in disordered quantum spin chains, arXiv:2602.00245.
  146. X. Wang, M. M. Wilde, and Y. Su, Quantifying the magic of quantum channels, New J. Phys. 21, 103002 (2019).
  147. A. Heimendahl, F. Montealegre-Mora, F. Vallentin, and D. Gross, Stabilizer extent is not multiplicative, Quantum 5, 400 (2021).
  148. D. Gross, Hudson's theorem for finite‐dimensional quantum systems, J. Math. Phys. 47, 122107 (2006).
  149. P. S. Tarabunga, Critical behaviors of non-stabilizerness in quantum spin chains, Quantum 8, 1413 (2024).
  150. X. Turkeshi, E. Tirrito, and P. Sierant, Magic spreading in random quantum circuits, Nat. Commun. 16, 2575 (2025).
  151. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, UK, 2002)
  152. C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, 3rd ed. (Springer, Berlin, 2004).
  153. X. Turkeshi and P. Sierant, Hilbert space delocalization under random unitary circuits, Entropy 26, 471 (2024).
  154. X. Turkeshi, Lecture notes on replica tensor networks for random quantum circuits, arXiv:2605.11150.
  155. M. P. A. Fisher, V. Khemani, A. Nahum, and S. Vijay, Random quantum circuits, Annu. Rev. Condens. Matter Phys. 14, 335 (2023).
  156. A. C. Potter and R. Vasseur, Entanglement dynamics in hybrid quantum circuits, in Entanglement in Spin Chains (Springer, Cham, 2022), pp. 211–249.
  157. H.-Z. Li, J.-X. Zhong, and X.-J. Yu, Measurement-induced entanglement phase transition in free fermion systems, J. Phys.: Condens. Matter 37, 273002 (2025).
  158. G. D. Giulio, X. Turkeshi, and S. Murciano, Measurement-induced symmetry restoration and quantum Mpemba effect, Entropy 27, 407 (2025).
  159. R. Travaglino, C. Rylands, and P. Calabrese, Quench dynamics of entanglement entropy under projective charge measurements: The free fermion case, J. Stat. Mech.: Theor. Exp. (2025) 123101.
  160. H. Yu, J. Hu, and S.-X. Zhang, Quantum Pontus-Mpemba effects in real- and imaginary-time dynamics, Phys. Rev. B 113, 134304 (2026).
  161. S. Aditya, A. Summer, P. Sierant, and X. Turkeshi, Data and code for “Mpemba effects in quantum complexity”, Zenodo, 2026, doi:10.5281/zenodo.21788287.
  162. A. Hamma, R. Ionicioiu, and P. Zanardi, Bipartite entanglement and entropic boundary law in lattice spin systems, Phys. Rev. A 71, 022315 (2005).
  163. A. Nahum, J. Ruhman, S. Vijay, and J. Haah, Quantum entanglement growth under random unitary dynamics, Phys. Rev. X 7, 031016 (2017).
  164. P. Sierant, M. Schirò, M. Lewenstein, and X. Turkeshi, Entanglement growth and minimal membranes in (d+1) random unitary circuits, Phys. Rev. Lett. 131, 230403 (2023).

Outline

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Phys. Rev. B 114, 074310– Published 25 August, 2026
  • Received 8 October 2025
  • Revised 1 June 2026
  • Accepted 3 August 2026
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