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arXiv · 1610.00581

Time and Space Efficient Quantum Algorithms for Detecting Cycles and Testing Bipartiteness

Chris Cade·Ashley Montanaro·Aleksandrs Belovs
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Abstract

We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms for deciding both properties in $\tilde{O}(n^{3/2})$ time and using $O(\log n)$ classical and quantum bits of storage in the adjacency matrix model. We then present quantum algorithms for deciding the two properties in the adjacency array model, which run in time $\tilde{O}(n\sqrt{d_m})$ and also require $O(\log n)$ space, where $d_m$ is the maximum degree of any vertex in the input graph.

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Chris Cade, Ashley Montanaro, Aleksandrs Belovs. 2016-10-03. Time and Space Efficient Quantum Algorithms for Detecting Cycles and Testing Bipartiteness. https://arxiv.org/abs/1610.00581

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