Edge-state enhanced transport in a 2-dimensional quantum walk

TL;DR

This paper demonstrates that cutting links along a line in a disordered 2D quantum walk creates topologically protected edge states, enabling efficient transport between two points despite disorder.

Contribution

It introduces a novel method of creating efficient quantum transport channels via edge states in disordered systems by link cutting, supported by topological analysis.

Findings

Edge states enable robust transport despite disorder.

Link cutting along a line induces topologically protected edge states.

The system's topological invariant is the quasienergy winding.

Abstract

Quantum walks on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder. We ask how to create an efficient transport channel from a fixed source site (A) to fixed target site (B) in a disordered 2-dimensional discrete-time quantum walk by cutting some of the links. We show that the somewhat counterintuitive strategy of cutting links along a single line connecting A to B creates such a channel. The efficient transport along the cut is due to topologically protected chiral edge states, which exist even though the bulk Chern number in this system vanishes. We give a realization of the walk as a periodically driven lattice Hamiltonian, and identify the bulk topological invariant responsible for the edge states as the quasienergy winding of this Hamiltonian.