Unitary equivalent classes of one-dimensional quantum walks

2016/03/18 by Hiromichi Ohno, Ohno, Hiromichi
Computer Science · Mathematics · Physics and Astronomy · #Blockchain Technology in Education and Learning #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1603.05778

arxiv created 2016/03/18 · openalex publication_date 2016/03/18 · arxiv updated 2016/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This study investigates unitary equivalent classes of one-dimensional quantum walks. We prove that one-dimensional quantum walks are unitary equivalent to quantum walks of Ambainis type and that translation-invariant one-dimensional quantum walks are Szegedy walks. We also present a necessary and sufficient condition for a one-dimensional quantum walk to be a Szegedy walk.

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