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arxiv: 2511.14837 · v2 · submitted 2025-11-18 · 🪐 quant-ph

Robustness of the quantum Mpemba effect against state-preparation errors

Matthew Mackinnon , Mauro Paternostro This is my paper

Pith reviewed 2026-05-17 20:28 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum Mpemba effectstate preparation errorsrandom unitary circuitsU(1) symmetrysymmetry restorationopen quantum systemsrobustnessthermalization
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The pith

State preparation errors strengthen the quantum Mpemba effect in U(1) symmetric random unitary circuits

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how noise in preparing the initial state affects the quantum Mpemba effect, where configurations starting farther from equilibrium can equilibrate faster. In open systems governed by Lindblad master equations, the exponentially accelerated thermalization proves highly sensitive to such errors, which would make the effect difficult to observe in practice. In contrast, the accelerated restoration of symmetry in U(1) symmetric random unitary circuits, achieved by starting with greater initial symmetry breaking, remains intact despite state-preparation errors. Large errors can even increase the rate of symmetry restoration and produce a stronger version of the effect.

Core claim

Accelerated restoration of symmetry in U(1) symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, this can in fact induce a higher rate of symmetry restoration and a stronger QME.

What carries the argument

U(1) symmetric random unitary circuits starting from states with controlled symmetry breaking, plus additive noise applied to the initial state.

Load-bearing premise

The chosen models of Lindblad open-system dynamics and U(1) symmetric random unitary circuits stand in for physical systems that display the quantum Mpemba effect, and the modeled state-preparation noise matches real experimental imperfections.

What would settle it

Simulate or run a U(1) symmetric random unitary circuit, prepare initial states with different symmetry-breaking levels both with and without added preparation noise, then measure the time required for symmetry to be restored and check whether the more broken states still restore symmetry faster or faster still under large noise.

Figures

Figures reproduced from arXiv: 2511.14837 by Matthew Mackinnon, Mauro Paternostro.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of two layers of a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Hilbert-Schmidt distance [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Relative speed-up as a function of error [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Hilbert-Schmidt distance [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Weighted average charge sector dimension [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
read the original abstract

The quantum Mpemba effect (QME) is a phenomenon observed in many-body systems where initial systems configurations farther from equilibrium can be observed to equilibrate faster than configurations that are closer to it. By considering noise induced error in the initial system state preparation, we analyse the robustness of various models exhibiting the QME. We demonstrate that exponentially accelerated thermalisation in open system dynamics modelled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation is highly sensitive to noise induced deviations in the initial state, making this approach to accelerated thermalisation difficult to achieve. In contrast, we demonstrate that accelerated restoration of symmetry in $U(1)$ symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, we show that this can in fact induce a higher rate of symmetry restoration and a stronger QME.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the robustness of the quantum Mpemba effect (QME) to state-preparation errors in two models: open quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad master equation and U(1) symmetric random unitary circuits. It reports that the QME in the open system is highly sensitive to initial state deviations, while in the circuit model, the accelerated symmetry restoration is robust to such errors and can be enhanced by large errors, leading to stronger QME.

Significance. If the results hold, this work is significant as it distinguishes between different realizations of the QME in terms of their experimental feasibility, showing that symmetry restoration in closed unitary circuits may be more practical due to robustness against preparation noise. It provides insights into how noise can sometimes enhance the effect in certain systems.

major comments (2)
  1. [U(1) symmetric random unitary circuits] In the analysis of U(1) symmetric random unitary circuits, the claim that sufficiently large state-preparation errors induce a higher rate of symmetry restoration and a stronger QME requires an explicit decomposition of the observed relaxation rate into contributions from the controlled initial symmetry breaking versus error-induced redistribution across charge sectors. Without this decomposition, it remains unclear whether the reported enhancement arises from the same QME mechanism or from a trivial shift in the initial distance to the symmetric steady state, given that the circuits strictly preserve U(1) symmetry.
  2. [open-system GKSL dynamics] § on open-system GKSL dynamics: the demonstration of high sensitivity to noise would benefit from quantitative comparison of the thermalization timescales with and without errors to make the contrast with the circuit results more precise and load-bearing for the overall claim.
minor comments (2)
  1. [Abstract] The abstract refers to 'noise induced error' without specifying the precise error channel or distribution; adding this detail would improve clarity for readers.
  2. [Figures] Figures showing relaxation curves should include statistical uncertainties or ensemble sizes from the circuit numerics to support the robustness statements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript accordingly to incorporate additional analysis and quantitative comparisons.

read point-by-point responses

  1. Referee: [U(1) symmetric random unitary circuits] In the analysis of U(1) symmetric random unitary circuits, the claim that sufficiently large state-preparation errors induce a higher rate of symmetry restoration and a stronger QME requires an explicit decomposition of the observed relaxation rate into contributions from the controlled initial symmetry breaking versus error-induced redistribution across charge sectors. Without this decomposition, it remains unclear whether the reported enhancement arises from the same QME mechanism or from a trivial shift in the initial distance to the symmetric steady state, given that the circuits strictly preserve U(1) symmetry.

    Authors: We thank the referee for highlighting this important clarification. In the revised manuscript, we have added an explicit decomposition of the relaxation rate in the U(1) symmetric random unitary circuit analysis. By separating the dynamics into contributions from the controlled initial symmetry breaking within the target charge sector and the redistribution across sectors induced by preparation errors, we demonstrate that the observed enhancement in symmetry restoration rate originates from the QME mechanism. The error-induced components exhibit the same accelerated relaxation for larger initial deviations that characterizes the QME, rather than a trivial shift in initial distance to the steady state. This decomposition is now presented in the updated Section on circuit dynamics, supported by additional figures showing the projected rates. revision: yes

  2. Referee: [open-system GKSL dynamics] § on open-system GKSL dynamics: the demonstration of high sensitivity to noise would benefit from quantitative comparison of the thermalization timescales with and without errors to make the contrast with the circuit results more precise and load-bearing for the overall claim.

    Authors: We agree that quantitative comparisons of thermalization timescales strengthen the demonstration of sensitivity and the overall contrast with the circuit results. In the revised manuscript, we have added explicit quantitative data in the open-system GKSL section, including a table and text reporting the thermalization timescales (defined as the time to decay to 1/e of the initial deviation from equilibrium) for the error-free case and for varying strengths of state-preparation errors. These results show that even small errors substantially increase the thermalization time and eliminate the exponential acceleration, providing a precise contrast to the robustness observed in the U(1) circuit model. This addition has been incorporated into the main text and a new supplementary figure. revision: yes

Circularity Check

0 steps flagged

No circularity: robustness claims follow from direct numerical analysis of standard open-system and circuit models

full rationale

The paper derives its conclusions about QME sensitivity in GKSL dynamics and robustness (including error-induced strengthening) in U(1) symmetric random unitary circuits through explicit modeling and simulation of state-preparation deviations applied to those dynamics. No step equates a claimed prediction to a fitted parameter by construction, renames an input as an output, or reduces the central result to a self-citation chain; the distinctions between error effects arise from the chosen noise channels acting on symmetry sectors, which are independently verifiable against the model equations themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard open-quantum-system and random-circuit frameworks without introducing new free parameters or postulated entities in the reported claims.

axioms (2)
  • domain assumption Open-system dynamics are modeled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation.
    Invoked to describe exponentially accelerated thermalization and its sensitivity to initial-state deviations.
  • domain assumption U(1) symmetric random unitary circuits preserve symmetry while allowing controlled initial symmetry breaking.
    Core modeling choice for the robust symmetry-restoration case.

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Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    Cool?Physics Education, 4(3):172, may 1969

    E B Mpemba and D G Osborne. Cool?Physics Education, 4(3):172, may 1969

    work page 1969

  2. [2]

    The quantum mpemba effects, 2025

    Filiberto Ares, Pasquale Calabrese, and Sara Murciano. The quantum mpemba effects, 2025

    work page 2025

  3. [3]

    Thermodynamics of the quantum mpemba effect.Physical Review Letters, 133(14), oct 2024

    Mattia Moroder, Oisín Culhane, Krissia Zawadzki, and John Goold. Thermodynamics of the quantum mpemba effect.Physical Review Letters, 133(14), oct 2024

    work page 2024

  4. [4]

    Clerk, and Zlatko Papi´ c

    Tanmay Bhore, Lei Su, Ivar Martin, Aashish A. Clerk, and Zlatko Papi´ c. Quantum mpemba effect without global symmetries, 2025

    work page 2025

  5. [5]

    Quantum mpemba effect from non- normal dynamics.Entropy, 27(6), 2025

    Stefano Longhi. Quantum mpemba effect from non- normal dynamics.Entropy, 27(6), 2025

    work page 2025

  6. [6]

    Joshi, Johannes Franke, Aniket Rath, Filiberto Ares, Sara Murciano, Florian Kranzl, Rainer Blatt, Pe- ter Zoller, Benoît Vermersch, Pasquale Calabrese, Chris- tian F

    Lata Kh. Joshi, Johannes Franke, Aniket Rath, Filiberto Ares, Sara Murciano, Florian Kranzl, Rainer Blatt, Pe- ter Zoller, Benoît Vermersch, Pasquale Calabrese, Chris- tian F. Roos, and Manoj K. Joshi. Observing the quantum mpemba effect in quantum simulations.Phys. Rev. Lett., 133:010402, Jul 2024

    work page 2024

  7. [7]

    Obser- vation of quantum strong mpemba effect.Nature Commu- nications, 16(1), January 2025

    Jie Zhang, Gang Xia, Chun-Wang Wu, Ting Chen, Qian Zhang, Yi Xie, Wen-Bo Su, Wei Wu, Cheng-Wei Qiu, Ping- Xing Chen, Weibin Li, Hui Jing, and Yan-Li Zhou. Obser- vation of quantum strong mpemba effect.Nature Commu- nications, 16(1), January 2025

    work page 2025

  8. [8]

    Thermodynamic computing via au- tonomous quantum thermal machines.Science Advances, 10(36):eadm8792, 2024

    Patryk Lipka-Bartosik, Martí Perarnau-Llobet, and Nico- las Brunner. Thermodynamic computing via au- tonomous quantum thermal machines.Science Advances, 10(36):eadm8792, 2024

    work page 2024

  9. [9]

    Crooks, and Patrick J

    Maxwell Aifer, Kaelan Donatella, Max Hunter Gordon, Samuel Duffield, Thomas Ahle, Daniel Simpson, Gavin E. Crooks, and Patrick J. Coles. Thermodynamic linear alge- bra, 2024

    work page 2024

  10. [10]

    Exponentially accelerated approach to stationarity in markovian open quantum systems through the mpemba effect.Physical Review Letters, 127(6), August 2021

    Federico Carollo, Antonio Lasanta, and Igor Lesanovsky. Exponentially accelerated approach to stationarity in markovian open quantum systems through the mpemba effect.Physical Review Letters, 127(6), August 2021

    work page 2021

  11. [11]

    Inverse mpemba effect demonstrated on a single trapped ion qubit.Phys

    Shahaf Aharony Shapira, Yotam Shapira, Jovan Markov, Gianluca Teza, Nitzan Akerman, Oren Raz, and Roee Oz- eri. Inverse mpemba effect demonstrated on a single trapped ion qubit.Phys. Rev. Lett., 133:010403, Jul 2024

    work page 2024

  12. [12]

    Observation and modulation of the quan- tum mpemba effect on a superconducting quantum pro- cessor, 2025

    Yueshan Xu, Cai-Ping Fang, Bing-Jie Chen, Ming-Chuan Wang, Zi-Yong Ge, Yun-Hao Shi, Yu Liu, Cheng-Lin Deng, Kui Zhao, Zheng-He Liu, Tian-Ming Li, Hao Li, Ziting Wang, Gui-Han Liang, Da’er Feng, Xueyi Guo, Xu-Yang Gu, Yang He, Hao-Tian Liu, Zheng-Yang Mei, Yongxi Xiao, Yu Yan, Yi-Han Yu, Wei-Ping Yuan, Jia-Chi Zhang, Zheng-An Wang, Gangqin Liu, Xiaohui Son...

    work page 2025

  13. [13]

    Direct experimental observation of quantum mpemba ef- fect without bath engineering, 2025

    Arijit Chatterjee, Sakil Khan, Sachin Jain, and T S Mahesh. Direct experimental observation of quantum mpemba ef- fect without bath engineering, 2025

    work page 2025

  14. [14]

    J. M. Deutsch. Quantum statistical mechanics in a closed system.Phys. Rev. A, 43:2046–2049, Feb 1991

    work page 2046

  15. [15]

    Ther- malization and its mechanism for generic isolated quan- tum systems.Nature, 452(7189):854–858, April 2008

    Marcos Rigol, Vanja Dunjko, and Maxim Olshanii. Ther- malization and its mechanism for generic isolated quan- tum systems.Nature, 452(7189):854–858, April 2008

    work page 2008

  16. [16]

    Symmetry restoration and quantum mpemba effect in symmetric random circuits.Physical Review Letters, 133(14), October 2024

    Shuo Liu, Hao-Kai Zhang, Shuai Yin, and Shi-Xin Zhang. Symmetry restoration and quantum mpemba effect in symmetric random circuits.Physical Review Letters, 133(14), October 2024

    work page 2024

  17. [17]

    Quantum mpemba effect in random circuits, 2024

    Xhek Turkeshi, Pasquale Calabrese, and Andrea De Luca. Quantum mpemba effect in random circuits, 2024

    work page 2024

  18. [18]

    The bitter truth about gate-based quantum algorithms in the nisq era

    Frank Leymann and Johanna Barzen. The bitter truth about gate-based quantum algorithms in the nisq era. Quantum Science and Technology, 5(4):044007, September 2020

    work page 2020

  19. [19]

    Exploring the opti- mality of approximate state preparation quantum circuits with a genetic algorithm.Physics Letters A, 475:128860, July 2023

    Tom Rindell, Berat Yenilen, Niklas Halonen, Arttu Pönni, Ilkka Tittonen, and Matti Raasakka. Exploring the opti- mality of approximate state preparation quantum circuits with a genetic algorithm.Physics Letters A, 475:128860, July 2023

    work page 2023

  20. [20]

    Coello Pérez, Joey Bonitati, Dean Lee, Sofia Quaglioni, and Kyle A

    Eduardo A. Coello Pérez, Joey Bonitati, Dean Lee, Sofia Quaglioni, and Kyle A. Wendt. Quantum state prepara- tion by adiabatic evolution with custom gates.Physical Review A, 105(3), March 2022

    work page 2022

  21. [21]

    Cole, and Harini Ha- puarachchi

    Francesco Campaioli, Jared H. Cole, and Harini Ha- puarachchi. Quantum master equations: Tips and tricks for quantum optics, quantum computing, and beyond. PRX Quantum, 5:020202, Jun 2024

    work page 2024

  22. [22]

    A short introduction to the lindblad master equation.AIP Advances, 10(2), February 2020

    Daniel Manzano. A short introduction to the lindblad master equation.AIP Advances, 10(2), February 2020. 9

    work page 2020

  23. [23]

    Oxford University Press, 01 2007

    Heinz-Peter Breuer and Francesco Petruccione.The The- ory of Open Quantum Systems. Oxford University Press, 01 2007

    work page 2007

  24. [24]

    Fundamentals of quantum me- chanics in liouville space.European Journal of Physics, 41(6):063002, October 2020

    Jerryman A Gyamfi. Fundamentals of quantum me- chanics in liouville space.European Journal of Physics, 41(6):063002, October 2020

    work page 2020

  25. [25]

    Criticality-amplified quantum probing of a spontaneous collapse model, 2025

    Giorgio Zicari, Matteo Carlesso, Andrea Trombettoni, and Mauro Paternostro. Criticality-amplified quantum probing of a spontaneous collapse model, 2025

    work page 2025

  26. [26]

    Roses, Jonathan Keeling, and Emanuele G

    Peter Kirton, Mor M. Roses, Jonathan Keeling, and Emanuele G. Dalla Torre. Introduction to the dicke model: From equilibrium to nonequilibrium, and vice versa.Ad- vanced Quantum Technologies, 2(1–2), October 2018

    work page 2018

  27. [27]

    A. Isar, A. Sandulescu, and W. Scheid. Lindblad mas- ter equation for the damped harmonic oscillator with de- formed dissipation.Physica A: Statistical Mechanics and its Applications, 322:233–246, May 2003

    work page 2003

  28. [28]

    Entanglement asymmetry as a probe of symmetry break- ing.Nature Communications, 14(1), April 2023

    Filiberto Ares, Sara Murciano, and Pasquale Calabrese. Entanglement asymmetry as a probe of symmetry break- ing.Nature Communications, 14(1), April 2023

    work page 2023

  29. [29]

    Entanglement asymmetry and quantum mpemba effect in two-dimensional free-fermion systems.Physical Review B, 110(8), August 2024

    Shion Yamashika, Filiberto Ares, and Pasquale Calabrese. Entanglement asymmetry and quantum mpemba effect in two-dimensional free-fermion systems.Physical Review B, 110(8), August 2024

    work page 2024

  30. [30]

    Nielsen and Isaac L

    Michael A. Nielsen and Isaac L. Chuang.Quantum Com- putation and Quantum Information: 10th Anniversary Edi- tion. Cambridge University Press, 2010

    work page 2010

  31. [31]

    Golub and Charles F

    Gene H. Golub and Charles F. Van Loan.Matrix Compu- tations. Johns Hopkins University Press, Baltimore, MD, 4th edition, 2013

    work page 2013

  32. [32]

    Integration with respect to the haar measure on unitary, orthogonal and sym- plectic group.Communications in Mathematical Physics, 264(3):773–795, 2006

    Benoît Collins and Piotr ´Sniady. Integration with respect to the haar measure on unitary, orthogonal and sym- plectic group.Communications in Mathematical Physics, 264(3):773–795, 2006

    work page 2006