$ε$-Uniform Mixing in Discrete Quantum Walks

• URL: http://arxiv.org/abs/2311.18797v3
• Date: Tue, 2 Jul 2024 17:58:06 GMT
• Title: $ε$-Uniform Mixing in Discrete Quantum Walks
• Abstract summary: We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform. We establish a characterization of this phenomenon on regular non-bipartite graphs in terms of their adjacency eigenvalues and eigenprojections.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $m\ge 2$.

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