The square and cube of the transition matrix of the discrete-time quantum walk on a graph
Yusuke Higuchi, Norio Konno, Iwao Sato, Etsuo Segawa · arXiv (Cornell University) · 2012
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of transition matrix of a classical random walk on vertices. Furthermore we determine the structure of the positive support of the cube of some evolution matrix, which is said to be useful for isospectral problem in graphs, under a certain condition.