Localized State in a Two-Dimensional Quantum Walk on a Disordered Lattice

TL;DR

This paper demonstrates a ten-step two-dimensional quantum walk with a localized state on a disordered lattice, using a novel experimental setup that simulates a single walker with a four-dimensional coin.

Contribution

It introduces an experimental realization of a 2D quantum walk with a localized state on a disordered lattice, using two 1D walks with shared coins as an analogy.

Findings

Successful implementation of a 10-step quantum walk on an 11x11 lattice

Observation of walker localization due to lattice disorder

Validation of the analogy between two 1D walks and a 2D walk with a four-dimensional coin

Abstract

We realize a pair of simultaneous ten-step one-dimensional quantum walks with two walkers sharing coins, which we prove is analogous to the ten-step two-dimensional quantum walk with a single walker holding a four-dimensional coin. Our experiment demonstrates a ten-step quantum walk over an 11x11 two-dimensional lattice with a line defect, thereby realizing a localized walker state.