Exact simulation of coined quantum walks with the continuous-time model
Abstract
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and taking appropriate limits. In this work, we produce the evolution of a coined quantum walk on a generic graph using a continuous-time quantum walk on a larger graph. In addition to expanding the underlying structure, we also have to switch on and off edges during the continuous-time evolution to accommodate the alternation between the shift and coin operators from the coined model. In one particular case, the connection is very natural, and the continuous-time quantum walk that simulates the coined quantum walk is driven by the graph Laplacian on the dynamically changing expanded graph.
Cite
@article{arxiv.1606.04030,
title = {Exact simulation of coined quantum walks with the continuous-time model},
author = {Pascal Philipp and Renato Portugal},
journal= {arXiv preprint arXiv:1606.04030},
year = {2016}
}