A counterintuitive role of geometry in transport by quantum walks

TL;DR

This paper reveals that increasing the transport distance or adding branches in quantum walks can unexpectedly improve transport efficiency, explained through trapped states in various geometries.

Contribution

It uncovers the counterintuitive impact of geometry on quantum transport efficiency and provides analytical explanations using trapped states.

Findings

Transport efficiency can be enhanced by increasing distance or adding branches.

Trapped states explain non-classical transport effects.

Geometries like ladder graphs and Cayley trees exhibit these phenomena.

Abstract

Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance between source and target or adding redundant branches to the actual graph may surprisingly result in a significant enhancement of transport efficiency. We explain analytically the observed non-classical effects using the concept of trapped states for several intriguing geometries including the ladder graph, the Cayley tree and its modifications.