Quantum walk in symmetric Cayley graph over $\Z_2^n$
Quantum Physics
2013-07-31 v2 Combinatorics
Abstract
We show that the hitting time of the discrete quantum walk on a symmetric Cayley graph over from a vertex to its antipodal is polynomial in degree of the graph. We prove that returning time of quantum walk on a symmetric Cayley graph over is polynomial and the probability to hit is almost one. To prove it, we give a new estimation of Kravchuk coefficients. We give an example of a probabilistic polynomial algorithm that finds an antipodal vertex in symmetric Cayley graphs.
Keywords
Cite
@article{arxiv.1305.6849,
title = {Quantum walk in symmetric Cayley graph over $\Z_2^n$},
author = {Ilnur Khuziev},
journal= {arXiv preprint arXiv:1305.6849},
year = {2013}
}