Exceptional configurations of quantum walks with Grover's coin
Quantum Physics
2015-09-24 v1
Abstract
We study search by quantum walk on a two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. We show what the most natural coin transformation - Grover's diffusion transformation - has a wide class of exceptional configurations of marked locations, for which the probability of finding any of the marked locations does not grow over time. This extends the class of known exceptional configurations; until now the only known such configuration was the "diagonal construction" by Ambainis and Rivosh [AR08]
Keywords
Cite
@article{arxiv.1509.06862,
title = {Exceptional configurations of quantum walks with Grover's coin},
author = {Nikolajs Nahimovs and Alexander Rivosh},
journal= {arXiv preprint arXiv:1509.06862},
year = {2015}
}
Comments
14 pages, 9 figures, 3 tables