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

TL;DR

This paper investigates the steady-state behavior of discrete-time quantum systems with stochastic resets, revealing unique resonance phenomena and conditions for steady state existence, with implications for quantum device engineering.

Contribution

It introduces a detailed analysis of discrete-time reset dynamics, including Poissonian and non-Poissonian resets, highlighting novel resonance effects and steady-state conditions in quantum systems.

Findings

Resonances in quantum gates enable non-diagonal steady states.

Steady states exist under Poissonian resets but not when reset probability diminishes rapidly.

Discrete-time reset dynamics differ fundamentally from continuous-time cases.

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.