Symmetries in discrete time quantum walks on Cayley graphs
  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. 
V\'aclav Poto\v{c}ek
quant-ph