Spectral Stability of Unitary Network Models

TL;DR

This paper reviews unitary network models across quantum computing and physics, demonstrating their spectral stability and universality, and establishing relationships among different models using advanced mathematical techniques.

Contribution

It introduces spectral stability results for a broad class of unitary models and shows the universality of symmetric quantum walks and CMV matrices.

Findings

Symmetric one-dimensional quantum walks are universal.

CMV matrices are also universal models.

Spectral stability and propagation properties are established for asymptotically uniform models.

Abstract

We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one dimensional quantum walks are universal, as are CMV matrices. We prove spectral stability and propagation properties for general asymptotically uniform models by means of unitary Mourre theory.