Spectral stability of unitary network models

Author:

Asch Joachim12,Bourget Olivier3,Joye Alain4

Affiliation:

1. Aix Marseille Université, CNRS, CPT UMR 7332, F–13288 Marseille cedex 9, France

2. Université de Toulon, CNRS, CPT UMR 7332, CS 60584, F-83041 Toulon Cedex 9, France

3. Departamento de Matemáticas Pontificia, Universidad Católica de Chile, Av. Vicuña, Mackenna 4860, C.P. 690 44 11, Macul Santiago, Chile

4. UJF-Grenoble 1, CNRS Institut Fourier UMR 5582, Grenoble, 38402, France

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

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