Quadratic speedup for finding marked vertices by quantum walks
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.
|Series||arXiv.org e-Print archive|
Ambainis, A, Gilyén, A.P, Jeffery, S, & Kokainis, M. (2019). Quadratic speedup for finding marked vertices by quantum walks. arXiv.org e-Print archive.