In this paper we study quantum state transfer (also called quantum tunneling) on graphs when there is a potential function on the vertex set. We present two main results. First, we show that for paths of length greater than three, there is no potential on the vertices of the path for which perfect state transfer between the endpoints can occur. In particular, this resolves (in the negative) a c...

Perfect (quantum) state transfer has been proved to be an effective model for quantum information processing. In this paper, we give a characterization of cubelike graphs having perfect edge (PEST, in short). By using lifting technique, show that every bent function, and some semi-bent functions as well, can produce PEST. Some concrete constructions such are provided. Notably, our method, one o...