Equivalence between discrete quantum walk models in arbitrary topologies
Quantum Physics
2011-07-18 v2 Mathematical Physics
math.MP
Abstract
Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in arbitrary topologies. Here we present a general construction for the two models for any graph and also for position dependent transition amplitudes. We then prove constructively their unitary equivalence. Defining appropriate projector operators, we moreover show how to obtain the probabilities for one model from the evolution of the other.
Cite
@article{arxiv.0911.0042,
title = {Equivalence between discrete quantum walk models in arbitrary topologies},
author = {F. M. Andrade and M. G. E. da Luz},
journal= {arXiv preprint arXiv:0911.0042},
year = {2011}
}
Comments
Revtex, 5 pages, 2 figures, published version