A Characterization of the Graphs to Induce Periodic Grover Walk

2017/03/18 by Yusuke Yoshie, Yoshie, Yusuke · 2 citations
Computer Science · Engineering · #Advanced Graph Theory Research #Cellular Automata and Applications #FOS: Physical sciences #Quantum Physics (quant-ph) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1703.06286

openalex publication_date 2017/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper explains the periodicity of the Grover walk on finite graphs. We characterize the graphs to induce 2, 3, 4, 5-periodic Grover walk and obtain a necessary condition of the graphs to induce an odd-periodic Grover walk.

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• Periodicity for the Fourier quantum walk on regular graphs
• Quantum Search on Simplicial Complexes

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• Odd-periodic Grover walk
• Regular graphs to induce even periodic Grover walks
• Periodicity of Grover walks on distance-regular graphs
• Periodicity of Grover walks on bipartite regular graphs with at most five distinct eigenvalues
• Periodicity of bipartite walk on biregular graphs with conditional spectra