Edge states in a two-dimensional quantum walk with disorder

Abstract

We investigate the effect of spatial disorder on the edge states localized at the interface between two topologically different regions. Rotation disorder can localize the quantum walk if it is strong enough to change the topology, otherwise the edge state is protected. Nonlinear spatial disorder, dependent on the walker's state, attracts the walk to the interface even for very large coupling, preserving the ballistic transport characteristic of the clean regime.

extended new version; 10 pages, 10 figures

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• Toward simulation of topological phenomenas with one-, two- and three-dimensional quantum walks
• Response to glassy disorder in coin on spread of quantum walker