A note on the spectral mapping theorem of quantum walk models

2016/04/03 by Kaname Matsue, Matsue, Kaname, Osamu Ogurisu +3
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Spectral Theory (math.SP) #math-ph #math.FA #math.MP #math.SP #quant-ph

paper · pdf · doi:10.48550/arxiv.1604.00581

17 pages

arxiv created 2016/04/03 · openalex publication_date 2016/04/03 · arxiv updated 2016/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the description of eigenspace of a quantum walk model U with an associating linear operator T in abstract settings of quantum walk including the Szegedy walk on graphs. In particular, we provide the spectral mapping theorem of U without the spectral decomposition of T. Arguments in this direction reveal the eigenspaces of U characterized by the generalized kernels of linear operators given by T.

Citations

• Unitary equivalent classes of one-dimensional quantum walks II

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