Quadratic speedup for finding marked vertices by quantum walks
Quantum Physics
2019-03-19 v1 Data Structures and Algorithms
Probability
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.
Cite
@article{arxiv.1903.07493,
title = {Quadratic speedup for finding marked vertices by quantum walks},
author = {Andris Ambainis and András Gilyén and Stacey Jeffery and Martins Kokainis},
journal= {arXiv preprint arXiv:1903.07493},
year = {2019}
}
Comments
21 pages, 7 figures