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arXiv · 2607.04207

Uniform mixing and $ε$-uniform mixing on cycles

Xiwang Cao·Cuiwen Zhu
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Abstract

We study continuous-time quantum walks on cycles. We prove two complementary results. Firstly, the cycle $C_9$ does not admit uniform mixing at any time. Using the similar idea and Dickson polynomials, we prove that $C_{15}$ does not admit uniform mixing at any time neither. Secondly, for every prime $p$, we show that the cycle $C_{p^2}$ admits $ε$-uniform mixing.

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Xiwang Cao, Cuiwen Zhu. 2026-07-05. Uniform mixing and $ε$-uniform mixing on cycles. https://arxiv.org/abs/2607.04207

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