Resonances, Recurrence Times and Steady States in Monitored Noisy Qubit Systems

TL;DR

This paper investigates how monitored noisy qubit systems exhibit quantized recurrence times and steady states, revealing how noise and sampling influence ergodicity breaking and state stabilization.

Contribution

It introduces a statistical-physics model explaining the effects of noise and sampling on recurrence times and steady states in monitored qubit systems, highlighting the role of revivals.

Findings

Recurrence times are integer-quantized in noiseless systems.

Weak noise causes deviations and inversion of expected dips near revivals.

Sampling time controls a crossover between infinite-temperature and low-temperature steady states.

Abstract

We study non-equilibrium steady states and recurrence times in noisy, stroboscopically monitored qubit systems using complete measurements. In the noiseless limit, recurrence times are integer-quantized, with dips to lower integers when sampling approaches revival conditions associated with ergodicity breaking. Using an IBM quantum platform, we find that quantization is robust when sampling far from revivals, but breaks down dramatically near revivals: even weak noise produces large deviations and can invert the expected dips into pronounced peaks. To explain this behavior, we formulate a statistical-physics model of monitored noisy circuits in which monitoring drives an effective infinite-temperature steady state while thermal-like relaxation competes to favor a low-temperature limit. We show that the sampling time tunes a crossover between these regimes, near revivals stabilizing low-temperature behavior, and far from revivals restoring infinite-temperature behavior -- with noise strength and detuning acting as coupled small parameters near resonance.