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arXiv · 1302.3143

Quantum Walks and Electric Networks

Aleksandrs Belovs
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Abstract

We prove that a quantum walk can detect the presence of a marked element in a graph in $O(\sqrt{WR})$ steps for any initial probability distribution on vertices. Here, $W$ is the total weight of the graph, and $R$ is the effective resistance. This generalizes the result by Szegedy that is only applicable if the initial distribution is stationary. We describe a time-efficient quantum algorithm for 3-distinctness based on these ideas.

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Aleksandrs Belovs. 2013-02-13. Quantum Walks and Electric Networks. https://arxiv.org/abs/1302.3143

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