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Bibliographic Details
Main Authors: Levine, Luke, Mesapam, Jessy Jacob, Mustico, Benjamin, Tamon, Christino, Tucker, Gabriel, Zhan, Hanmeng
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.04414
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Table of 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 $K_2$.