Implementation of a spatial two-dimensional quantum random walk with tunable decoherence

TL;DR

This paper presents a scalable optical setup for two-dimensional quantum random walks with tunable decoherence, enabling exploration of quantum, classical, and localized behaviors in a controlled environment.

Contribution

It introduces a novel, versatile experimental scheme using simple optical components and a spatial light modulator to control decoherence in quantum walks.

Findings

Demonstrates control over quantum and classical walk regimes

Shows observation of Anderson localization under static disorder

Provides a scalable platform for quantum walk experiments

Abstract

We put forward a new, versatile and highly-scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small number of simple optical components arranged in a multi-path Mach-Zehnder-like configuration, where a weak coherent state with average photon number of 1 is injected. Environmental effects (decoherence) are generated by a spatial light modulator, which introduces pure dephasing in the transverse spatial plane, perpendicular to the direction of propagation of the light beam. By controlling the characteristics of this dephasing, one can explore a great variety of scenarios of quantum random walks: pure quantum evolution (ballistic spread), fast fluctuating environment leading to a diffusive classical random walk, and static disorder resulting in the observation of Anderson localization.