Dynamical Localization for General Scattering Quantum Walks

TL;DR

This paper proves dynamical localization for a broad class of quantum walks on infinite graphs with random phases, using fractional moment estimates and eigenfunction correlators for random unitary operators.

Contribution

It introduces a general framework for scattering quantum walks on arbitrary graphs with random phases and establishes dynamical localization results in high-disorder regimes.

Findings

Proves dynamical localization for random scattering quantum walks.

Establishes a relation between fractional moments and eigenfunction correlators.

Extends localization results to general infinite graphs with random unitary operators.

Abstract

We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum walk. We prove dynamical localization for random scattering walks in a large-disorder regime. The result is based on a relation between fractional moment estimates and eigenfunction correlators of independent interest, which we establish for general random unitary operators.