Odd-periodic Grover walk

2021/06/12 by Yusuke Yoshie, Yoshie, Yusuke · 3 citations
Computer Science · Physics and Astronomy · #05C50 #05C81 #81Q99 #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2106.06710

openalex publication_date 2021/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Grover walk is one of the most well-studied quantum walks on graphs. In this paper, we investigate its periodicity to reveal the relationship between the quantum walk and the underlying graph, focusing particularly on the characterization of graphs exhibiting a periodic Grover walk. Graphs having a periodic Grover walk with periods of 2, 3, 4, and 5 have previously been characterized. It is expected that graphs exhibiting a periodic Grover walk with odd period correspond to cycles with odd length. We address that problem and are able to perfectly characterize the class of graphs exhibiting an odd-periodic Grover walk by using a combinatorial method.

Cited by

• Subspace State Transfer in Coined Quantum Walks
• Pretty good state transfer in Grover walks on abelian Cayley graphs
• Perfect state transfer in Grover walks on association schemes and distance-regular graphs

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