Quantum walks with an anisotropic coin II: scattering theory

TL;DR

This paper develops a scattering theory framework for anisotropic quantum walks, analyzing their asymptotic behavior and including various models like defect and topological walks.

Contribution

It introduces an abstract scattering theory framework for anisotropic quantum walks, covering models like defect, two-phase, and topological walks.

Findings

Proves a weak limit theorem for asymptotic velocity.

Establishes a scattering analysis applicable to various quantum walk models.

Provides a new mathematical framework for studying quantum walk dynamics.

Abstract

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.