Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems

Sascha Wald; Louie Hong Yao; Thierry Platini; Chris Hooley; Federico Carollo

doi:10.22331/q-2025-05-13-1742

Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems

Sascha Wald^1,2, Louie Hong Yao³, Thierry Platini^1,2, Chris Hooley^1,2, and Federico Carollo^1,2

¹Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 2TT, United Kingdom
²$\mathbb{L}^4$ Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, Europe
³Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, VA 24061, USA

Published:	2025-05-13, volume 9, page 1742
Editor:	Alessio Benavoli
Eprint:	arXiv:2410.11497v3
Doi:	https://doi.org/10.22331/q-2025-05-13-1742
Citation:	Quantum 9, 1742 (2025).

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Abstract

Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit reset. The possibility of realizing discrete-time reset dynamics on quantum computers makes it important to investigate the steady-state properties of such dynamics. Here, we explore the behavior of generic discrete-time unitary dynamics interspersed by random reset events. For Poissonian resets, we compute the stationary state of the process and demonstrate, by taking a weak-reset limit, the existence of "resonances" in the quantum gates, allowing for the emergence of steady state density matrices which are not diagonal in the eigenbasis of the generator of the unitary gate. Such resonances are a genuine discrete-time feature and impact on quantum and classical correlations even beyond the weak-reset limit. Furthermore, we consider non-Poissonian reset processes and explore conditions for the existence of a steady state. We show that, when the reset probability vanishes sufficiently rapidly with time, the system does not approach a steady state. Our results highlight key differences between continuous-time and discrete-time stochastic resetting and may be useful to engineer states with controllable correlations on existing devices.

Popular summary

Many modern quantum devices operate using gates, which means that their time-evolution is effectively discrete. Part of that discrete evolution is resetting – the reinitialization of certain qubits at particular points during the computation – and this can itself generate correlations between the qubits. Most of the literature on resetting-induced correlations, however, is for the continuous-time case; here we show that correlation features are drastically different in discrete-time dynamics with stochastic resetting.

Specifically, we consider a quantum gate that acts repeatedly on a set of qubits, evolving them in time. The dynamics due to this gate is stochastically interrupted by resetting events. Whether this mixed dynamics leads to a steady state at all depends on how the reset probability varies with the time since the last reset event: we conjecture general conditions for a steady state to exist. One case in which it certainly exists is when the reset probability is constant. In this case we show analytically that the steady state has features that are qualitatively different from its continuous-time counterpart due to resonant eigenspaces in the gate generator. We explore these differences in a two-qubit system with various types of gate, and find that there are fingerprints of the resonances in the correlation, entanglement, and discord structure.

Our results demonstrate crucial differences between the effects of continuous- and discrete-time resetting in quantum systems. They pave the way to design quantum states with controllable correlations and to investigate genuine many-body correlations in discrete-time systems.

► BibTeX data

@article{Wald2025stochasticresetting,
  doi = {10.22331/q-2025-05-13-1742},
  url = {https://doi.org/10.22331/q-2025-05-13-1742},
  title = {Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems},
  author = {Wald, Sascha and Yao, Louie Hong and Platini, Thierry and Hooley, Chris and Carollo, Federico},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1742},
  month = may,
  year = {2025}
}

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[1] Marcel Cech, Cecilia De Fazio, María Cea, Mari Carmen Bañuls, Igor Lesanovsky, and Federico Carollo, "Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems", Physical Review A 113 6, L060201 (2026).

[2] Sayan Roy, Shamik Gupta, and Giovanna Morigi, "Causality, localization, and universality of monitored quantum walks with long-range hopping", Physical Review E 112 4, 044146 (2025).

[3] Quancheng Liu, Sabine Tornow, David A. Kessler, and Eli Barkai, "Fractionally quantized recurrence detection times in monitored quantum many-body systems", Proceedings of the National Academy of Sciences 123 22, e2529694123 (2026).

[4] David Soldner, Igor Lesanovsky, and Gabriele Perfetto, "Nonanaliticities and ergodicity breaking in noninteracting many-body dynamics via stochastic resetting and global measurements", Physical Review E 114 1, 014105 (2026).

[5] Ruoyu Yin, Qingyuan Wang, Sabine Tornow, and Eli Barkai, "Resonances of recurrence time of monitored quantum walks", The Journal of Chemical Physics 162 24, 244114 (2025).

[6] Eli Chertkov, Andrew C. Potter, David Hayes, and Michael Foss-Feig, "Error detection without postselection in adaptive quantum circuits", Physical Review Research 8 2, 023057 (2026).

[7] Gabriele de Mauro, Marco Biroli, Satya N. Majumdar, and Grégory Schehr, "Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols", Physical Review E 113 1, 014120 (2026).

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