Exciton-mediated quantum search on a star graph

A fast and efficient quantum search algorithm is established by using the ability of an exciton to propagate along a star graph that exhibits two identical energetic defects. The first defect lies on the well-defined input site where the exciton is initially created, whereas the second defect occupies the target site whose unknown position must be determined. It is shown that when the energetic defects are judiciously chosen, specific quantum interferences arise so that the probability to observe the exciton on the target site becomes close to unity at a very short time t*. Consequently, a measurement of the exciton quantum state at time t* will reveal the identity of the position of the target site. The key point is that t* is the shortest time independent on the size of the graph that is physically accessible to the exciton to tunnel.