$ε$-Uniform Mixing in Discrete Quantum Walks
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866913412633591808 |
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| author | Zhan, Hanmeng |
| author_facet | Zhan, Hanmeng |
| contents | We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of this phenomenon on regular non-bipartite graphs in terms of their adjacency eigenvalues and eigenprojections. Using theory from association schemes, we show this phenomenon happens on a strongly regular graph $X$ if and only if $X$ or $\overline{X}$ has parameters $(4m^2, 2m^2\pm m, m^2\pm m, m^2\pm m)$ where $m\ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18797 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $ε$-Uniform Mixing in Discrete Quantum Walks Zhan, Hanmeng Combinatorics Discrete Mathematics Quantum Physics We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of this phenomenon on regular non-bipartite graphs in terms of their adjacency eigenvalues and eigenprojections. Using theory from association schemes, we show this phenomenon happens on a strongly regular graph $X$ if and only if $X$ or $\overline{X}$ has parameters $(4m^2, 2m^2\pm m, m^2\pm m, m^2\pm m)$ where $m\ge 2$. |
| title | $ε$-Uniform Mixing in Discrete Quantum Walks |
| topic | Combinatorics Discrete Mathematics Quantum Physics |
| url | https://arxiv.org/abs/2311.18797 |