Recurrence in discrete-time quantum stochastic walks

TL;DR

This paper investigates how classical randomness affects recurrence in discrete-time quantum stochastic walks, revealing conditions where classical noise suppresses recurrence probability and demonstrating quantum walks can outperform classical and purely quantum walks.

Contribution

It uncovers the counterintuitive effect of classical randomness reducing recurrence in quantum walks and characterizes the conditions for this phenomenon.

Findings

Classical randomness can decrease recurrence probability in quantum walks.

Recurrence suppression is a robust, asymptotic feature.

Quantum stochastic walks can outperform classical and quantum walks in certain tasks.

Abstract

Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which is a quantum stochastic process that interpolates between quantum and classical walk dynamics. Surprisingly, we find that introducing classical randomness can reduce the recurrence probability -- despite the fact that the classical random walk returns with certainty -- and we identify the conditions under which this intriguing phenomenon occurs. Numerical evaluation of the first-return generating function allows us to investigate the asymptotics of the return probability as the step number approaches infinity. This provides strong evidence that the suppression of recurrence probability is not a transient effect but a robust feature of the underlying quantum-classical interplay in the asymptotic limit. Our results show that for certain tasks discrete-time quantum stochastic walks outperform both classical random walks and unitary quantum walks.