Discrete-time Quantum Walks in random artificial Gauge Fields

TL;DR

This paper investigates how randomness in artificial gauge fields affects discrete-time quantum walks, showing that randomness induces decoherence and causes the walks to behave classically over time, with exact calculations of diffusion.

Contribution

It introduces a new analytical method to determine the equations of motion for average density operators in quantum walks with random gauge fields.

Findings

Randomness induces decoherence in quantum walks.

Quantum walks asymptotically behave like classical random walks.

Exact asymptotic diffusion coefficients are computed.

Abstract

Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical determination of the equations of motion obeyed by the average density operator. It is proven that randomness induces decoherence and that the quantum walks behave asymptotically like classical random walks. Asymptotic diffusion coefficients are computed exactly. The continuous limit is also obtained and discussed.