Periodicity and absolute zeta functions of multi-state Grover walks on cycles
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917906935185408 |
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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 |