The continuous-time quantum walk on some graphs based on the view of quantum probability

In this paper, continuous-time quantum walk is discussed based on the view of quantum probability, i.e. the quantum decomposition of the adjacency matrix A of graph. Regard adjacency matrix A as Hamiltonian which is a real symmetric matrix with elements 0 or 1, so we regard e(-itA) as an unbiased evolution operator, which is related to the calculation of probability amplitude. Combining the quantum decomposition and spectral distribution mu of adjacency matrix A, we calculate the probability amplitude reaching each stratum in continuous-time quantum walk on complete bipartite graphs, finite two-dimensional lattices, binary tree, N-ary tree and N-fold star power G*(N). Of course, this method is also suitable for studying some other graphs, such as growing graphs, hypercube graphs and so on, in addition, the applicability of this method is also explained.