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arXiv · 1903.07493

Quadratic speedup for finding marked vertices by quantum walks

Andris Ambainis·András Gilyén·Stacey Jeffery·Martins Kokainis
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Abstract

A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element quadratically faster than a classical random walk were only known for the special case when the marked set consists of just a single vertex, or in the case of some specific graphs. We present a new quantum algorithm for finding a marked vertex in any graph, with any set of marked vertices, that is (up to a log factor) quadratically faster than the corresponding classical random walk.

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Andris Ambainis, András Gilyén, Stacey Jeffery, Martins Kokainis. 2019-03-18. Quadratic speedup for finding marked vertices by quantum walks. https://arxiv.org/abs/1903.07493

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