A simple model of quantum walk with a gap in distribution
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912550732431360 |
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| author | Machida, Takuya |
| author_facet | Machida, Takuya |
| contents | Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding probabilities have been investigated and some interesting things have been analytically discovered. They are, for instance, ballistic behavior, localization, or a gap. We study a 1-dimensional quantum walk in this paper. Although the walker launches off a location under a localized initial state, some numerical experiments show that the quantum walker does not seem to distribute around the launching location, which suggests that the probability distribution holds a gap around the launching location. To prove the gap analytically, we derive a long-time limit distribution, from which one can tell more details about the finding probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A simple model of quantum walk with a gap in distribution Machida, Takuya Quantum Physics Mathematical Physics Probability Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding probabilities have been investigated and some interesting things have been analytically discovered. They are, for instance, ballistic behavior, localization, or a gap. We study a 1-dimensional quantum walk in this paper. Although the walker launches off a location under a localized initial state, some numerical experiments show that the quantum walker does not seem to distribute around the launching location, which suggests that the probability distribution holds a gap around the launching location. To prove the gap analytically, we derive a long-time limit distribution, from which one can tell more details about the finding probability. |
| title | A simple model of quantum walk with a gap in distribution |
| topic | Quantum Physics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2503.08151 |