Efficient quantum walk on the grid with multiple marked elements
Quantum Physics
2017-07-04 v1 Data Structures and Algorithms
Abstract
We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known quantum walk that finds a marked element in a number of steps less than the square-root of the extended hitting time. We also give a new tighter upper bound on the extended hitting time of a marked subset, expressed in terms of the hitting times of its members.
Cite
@article{arxiv.1612.08958,
title = {Efficient quantum walk on the grid with multiple marked elements},
author = {Peter Hoyer and Mojtaba Komeili},
journal= {arXiv preprint arXiv:1612.08958},
year = {2017}
}
Comments
18 pages, to appear in STACS 2017, the 34th International Symposium on Theoretical Aspects of Computer Science