Periodicity and absolute zeta functions of multi-state Grover walks on cycles

Fuente: arXiv
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Main Authors: Akahori, Jirô, Konno, Norio, Sato, Iwao, Tamura, Yuma
Format: Preprint
Published: 2025
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author Akahori, Jirô
Konno, Norio
Sato, Iwao
Tamura, Yuma
author_facet Akahori, Jirô
Konno, Norio
Sato, Iwao
Tamura, Yuma
contents Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions of Grover walks on cycle graphs. Specifically, we investigate Grover walks with an odd number of states and determine their periods for cycles with any number of vertices greater than or equal to two. In addition, we compute the absolute zeta functions of M-type Grover walks with finite periods. These results advance the understanding of the properties of Grover walks and their connection to absolute zeta functions.
format Preprint
id arxiv_https___arxiv_org_abs_2501_18600
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Periodicity and absolute zeta functions of multi-state Grover walks on cycles
Akahori, Jirô
Konno, Norio
Sato, Iwao
Tamura, Yuma
Quantum Physics
Mathematical Physics
Combinatorics
Probability
Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions of Grover walks on cycle graphs. Specifically, we investigate Grover walks with an odd number of states and determine their periods for cycles with any number of vertices greater than or equal to two. In addition, we compute the absolute zeta functions of M-type Grover walks with finite periods. These results advance the understanding of the properties of Grover walks and their connection to absolute zeta functions.
title Periodicity and absolute zeta functions of multi-state Grover walks on cycles
topic Quantum Physics
Mathematical Physics
Combinatorics
Probability
url https://arxiv.org/abs/2501.18600