From Disordered Quantum Walk to Physics of Off-diagonal Disorder

TL;DR

This paper investigates the unique localization and delocalization phenomena in off-diagonal disordered quantum walks, demonstrating key features through theoretical, computational, and experimental approaches, including a protocol to generate delocalized zero-modes.

Contribution

It provides a detailed analysis of off-diagonal disorder effects in quantum walks and proposes an adiabatic method to create delocalized zero-modes from localized states.

Findings

Quantum walk dynamics exhibit off-diagonal disorder features.

A protocol to generate delocalized zero-modes is demonstrated.

Numerical experiments support theoretical predictions.

Abstract

Systems with purely off-diagonal disorder have peculiar features such as the localization-delocalization transition and long-range correlations in their wavefunctions. To motivate possible experimental studies of the physics of off-diagonal disorder, we study in detail disordered discrete-time quantum walk in a finite chain, where the diagonal disorder can be set to zero by construction. Starting from a transfer matrix approach, we show, both theoretically and computationally, that the dynamics of the quantum walk with disorder manifests all the main features of off-diagonal disorder. We also propose how to prepare a remarkable delocalized zero-mode from a localized and easy-to-prepare initial state using an adiabatic protocol that increases the disorder strength slowly. Numerical experiments are also performed with encouraging results.