  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 state transfer. By using a lifting
technique, we show that every bent function, and some semi-bent functions as
well, can produce some graphs having PEST. Some concrete constructions of such
graphs are provided. Notably, using our method, one can obtain some classes of
infinite graphs possessing PEST.
