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We put forward a new, versatile and highly-scalable experimental setup forthe realization of discrete two-dimensional quantum random walks with asingle-qubit coin and tunable degree of decoherence. The proposed scheme makesuse of a small number of simple optical components arranged in a multi-pathMach-Zehnder-like configuration, where a weak coherent state with averagephoton number of 1 is injected. Environmental effects (decoherence) aregenerated by a spatial light modulator, which introduces pure dephasing in thetransverse spatial plane, perpendicular to the direction of propagation of thelight beam. By controlling the characteristics of this dephasing, one canexplore a great variety of scenarios of quantum random walks: pure quantumevolution (ballistic spread), fast fluctuating environment leading to adiffusive classical random walk, and static disorder resulting in theobservation of Anderson localization.

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