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

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.

11 pages, 5 figures, accepted for publication in Quantum, two references added

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Cited by in corpus (7)

• Resonances of recurrence time of monitored quantum walks
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems
• Error detection without post-selection in adaptive quantum circuits
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems
• Nonequilibrium phases and quantum correlations in synthetic transport models