Quantum Walks on Trees with Disorder: Decay, Diffusion, and Localization

TL;DR

This paper investigates how static disorder affects quantum walks on trees, revealing a transition from decay to diffusion and eventually to localization, highlighting the impact of imperfections on quantum transport efficiency.

Contribution

It provides a numerical analysis of disorder effects on quantum walks on trees, identifying the transition points between decay, diffusion, and localization regimes.

Findings

Small disorder causes quantum decay rather than localization.

Intermediate disorder leads to diffusive transport.

Large disorder induces Anderson localization.

Abstract

Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We numerically study the effect of static disorder on a quantum walk on the glued trees graph. For small disorder, we find that the dominant effect is a type of quantum decay, and not quantum localization. For intermediate disorder, there is a crossover to diffusive transport, while a localization transition is observed at large disorder, in agreement with Anderson localization on the Cayley tree.