English

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 Z2n\Z_2^n 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 Z2n\Z_2^n 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}
}