Directivity of Quantum Walk via Its Random Walk Replica
Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as quantum-walk-replicating random walks (QWRWs), have been studied in the lit...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/9021583 |
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| _version_ | 1832562436406771712 |
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| author | Tomoki Yamagami Etsuo Segawa Nicolas Chauvet André Röhm Ryoichi Horisaki Makoto Naruse |
| author_facet | Tomoki Yamagami Etsuo Segawa Nicolas Chauvet André Röhm Ryoichi Horisaki Makoto Naruse |
| author_sort | Tomoki Yamagami |
| collection | DOAJ |
| description | Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as quantum-walk-replicating random walks (QWRWs), have been studied in the literature where the eventual properties of QWRW coincide with those of QWs. However, we consider that the unique attributes of QWRWs have not been fully utilized in the former studies to obtain deeper or new insights into QWs. In this paper, we highlight the directivity of one-dimensional discrete quantum walks via QWRWs. By exploiting the fact that QWRW allows trajectories of individual walkers to be considered, we first discuss the determination of future directions of QWRWs, through which the effect of linear spreading and localization is manifested in another way. Furthermore, the transition probabilities of QWRWs can also be visualized and show a highly complex shape, representing QWs in a novel way. Moreover, we discuss the first return time to the origin between RWs and QWs, which is made possible via the notion of QWRWs. We observe that the first return time statistics of QWs are quite different from RWs, caused by both the linear spreading and localization properties of QWs. |
| format | Article |
| id | doaj-art-ef8f16d50d1847aebc8e75a7d6ad9df4 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ef8f16d50d1847aebc8e75a7d6ad9df42025-02-03T01:22:42ZengWileyComplexity1099-05262022-01-01202210.1155/2022/9021583Directivity of Quantum Walk via Its Random Walk ReplicaTomoki Yamagami0Etsuo Segawa1Nicolas Chauvet2André Röhm3Ryoichi Horisaki4Makoto Naruse5Department of Information Physics and ComputingGraduate School of Environment and Information SciencesDepartment of Information Physics and ComputingDepartment of Information Physics and ComputingDepartment of Information Physics and ComputingDepartment of Information Physics and ComputingQuantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as quantum-walk-replicating random walks (QWRWs), have been studied in the literature where the eventual properties of QWRW coincide with those of QWs. However, we consider that the unique attributes of QWRWs have not been fully utilized in the former studies to obtain deeper or new insights into QWs. In this paper, we highlight the directivity of one-dimensional discrete quantum walks via QWRWs. By exploiting the fact that QWRW allows trajectories of individual walkers to be considered, we first discuss the determination of future directions of QWRWs, through which the effect of linear spreading and localization is manifested in another way. Furthermore, the transition probabilities of QWRWs can also be visualized and show a highly complex shape, representing QWs in a novel way. Moreover, we discuss the first return time to the origin between RWs and QWs, which is made possible via the notion of QWRWs. We observe that the first return time statistics of QWs are quite different from RWs, caused by both the linear spreading and localization properties of QWs.http://dx.doi.org/10.1155/2022/9021583 |
| spellingShingle | Tomoki Yamagami Etsuo Segawa Nicolas Chauvet André Röhm Ryoichi Horisaki Makoto Naruse Directivity of Quantum Walk via Its Random Walk Replica Complexity |
| title | Directivity of Quantum Walk via Its Random Walk Replica |
| title_full | Directivity of Quantum Walk via Its Random Walk Replica |
| title_fullStr | Directivity of Quantum Walk via Its Random Walk Replica |
| title_full_unstemmed | Directivity of Quantum Walk via Its Random Walk Replica |
| title_short | Directivity of Quantum Walk via Its Random Walk Replica |
| title_sort | directivity of quantum walk via its random walk replica |
| url | http://dx.doi.org/10.1155/2022/9021583 |
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