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arXiv · 0708.2096

Non-uniform mixing of quantum walk on cycles

William Adamczak·Kevin Andrew·Leon Bergen·Dillon Ethier·Peter Hernberg·Jennifer Lin·Christino Tamon
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Abstract

A classical lazy random walk on cycles is known to mix to the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibit strong non-uniform mixing properties. Our results include the following: - The instantaneous distribution of a quantum walk on most even-length cycles is never uniform. - The average distribution of a quantum walk on any Abelian circulant graph is never uniform. As a corollary, the average distribution of a quantum walk on any standard circulant graph, such as the cycles, complete graphs, and even hypercubes, is never uniform.

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William Adamczak, Kevin Andrew, Leon Bergen, Dillon Ethier, Peter Hernberg, Jennifer Lin, Christino Tamon. 2007-08-15. Non-uniform mixing of quantum walk on cycles. https://arxiv.org/abs/0708.2096

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