If X is a graph with adjacency matrix A , then we define H ( t ) to be the operator exp ( i t A ) . We say that we have perfect state transfer in X from the vertex u to the vertex v at time ? if the u v -entry of | H ( ? ) u , v | = 1 . State transfer has been applied to key distribution in commercial cryptosystems, and it seems likely that other applications will be found. We offer a survey of some of the work on perfect state transfer and related questions. The emphasis is almost entirely on the mathematics. Highlights? We survey the interactions between graph theory and perfect state transfer. ? Perfect state transfer is of interest in quantum computing. ? We include some new results and open questions.
['Chris D. Godsil']
State transfer on graphs