Uniform Mixing in Chiral Quantum Walks
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910227854524416 |
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| author | Levine, Luke Mesapam, Jessy Jacob Mustico, Benjamin Tamon, Christino Tucker, Gabriel Zhan, Hanmeng |
| author_facet | Levine, Luke Mesapam, Jessy Jacob Mustico, Benjamin Tamon, Christino Tucker, Gabriel Zhan, Hanmeng |
| contents | This paper studies uniform mixing in continuous-time quantum walks. We show that for some unitary signing $σ$, the complete graph $K^σ_n$ has probabilistic uniform mixing. In contrast, Ahmadi \etal (2003) proved that no complete graph has uniform mixing except for $K_2$, $K_3$, and $K_4$. Our technique is based on a stopping rule for quantum walks which reduces global to local uniform mixing. As a corollary, we found an orientation of $H(n,4)$ that mixes to uniform faster than any other Hamming graphs, which improves a result of Godsil and Zhan (2019). We also show that there are infinite families of oriented circulants with average uniform mixing. This is a chiral violation of a No-Go theorem due to Godsil (2013) which states that no graph has average uniform mixing except for $K_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04414 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform Mixing in Chiral Quantum Walks Levine, Luke Mesapam, Jessy Jacob Mustico, Benjamin Tamon, Christino Tucker, Gabriel Zhan, Hanmeng Combinatorics Quantum Physics 05C50 This paper studies uniform mixing in continuous-time quantum walks. We show that for some unitary signing $σ$, the complete graph $K^σ_n$ has probabilistic uniform mixing. In contrast, Ahmadi \etal (2003) proved that no complete graph has uniform mixing except for $K_2$, $K_3$, and $K_4$. Our technique is based on a stopping rule for quantum walks which reduces global to local uniform mixing. As a corollary, we found an orientation of $H(n,4)$ that mixes to uniform faster than any other Hamming graphs, which improves a result of Godsil and Zhan (2019). We also show that there are infinite families of oriented circulants with average uniform mixing. This is a chiral violation of a No-Go theorem due to Godsil (2013) which states that no graph has average uniform mixing except for $K_2$. |
| title | Uniform Mixing in Chiral Quantum Walks |
| topic | Combinatorics Quantum Physics 05C50 |
| url | https://arxiv.org/abs/2605.04414 |