Unitary equivalence classes of split-step quantum walks

TL;DR

This paper classifies split-step quantum walks into unitary equivalence classes, providing explicit forms and extending the classification to Suzuki's SSQW, thereby deepening understanding of their structural properties.

Contribution

It introduces a comprehensive classification of all split-step quantum walks, including Suzuki's, based on their unitary equivalence, with explicit forms provided.

Findings

Explicit forms of quantum walks in the new class

Classification of unitary equivalence classes for SSQW

Extension of classification to Suzuki's SSQW

Abstract

This study investigates the unitary equivalence of split-step quantum walks (SSQW). We consider a new class of quantum walks which includes all SSQWs. We show the explicit form of quantum walks in this class, and clarify their unitary equivalence classes. Unitary equivalence classes of Suzuki's SSQW are also given.