Symmetries in discrete time quantum walks on Cayley graphs
arXiv:1211.0172
Abstract
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting a constructive method of finding all solutions of the problem with minimal additional assumptions. We apply the results on an example of a quantum walk on a line to demonstrate the practical significance of the theory.
11 pages