1207.4987 (Norio Konno et al.)

The square and cube of the transition matrix of the discrete-time
quantum walk on a graph    [PDF]

Norio Konno, Iwao Sato

We give a new proof of a determinant expression for the second weighted zeta function of a graph by using the method of Watanabe and Fukumizu. Also, we give another proof of a result by Emms et al. on spectra of the square of the transition matrix. Furthermore, we determine the structure of the positive supports of the cube of the transition matrix under a certain condition.

View original: http://arxiv.org/abs/1207.4987