Edge states in a two-dimensional quantum walk with disorder

TL;DR

This paper studies how different types of spatial disorder affect edge states in a 2D quantum walk, revealing conditions for localization, protection, and transport preservation of these states.

Contribution

It introduces analysis of rotation and nonlinear spatial disorder effects on topologically protected edge states in quantum walks.

Findings

Strong rotation disorder can localize the walk by changing topology.

Nonlinear disorder preserves ballistic transport even at high coupling.

Edge states remain protected under certain disorder conditions.

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.