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Periodicity for the Fourier quantum walk on regular graphs

2018/11/08 by Kei Saito, Saito, Kei
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.1811.03235

openalex publication_date 2018/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantum walks determined by the coin operator on graphs have been intensively studied. The typical examples of coin operator are the Grover and Fourier matrices. The periodicity of the Grover walk is well investigated. However, the corresponding result on the Fourier walk is not known. In this paper, we present a necessary condition for the Fourier walk on regular graphs to have the finite period. As an application of our result, we show that the Fourier walks do not have any finite period for some classes of regular graphs such as complete graphs, cycle graphs with selfloops, and hypercubes.

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