Spatial search on Johnson graphs by continuous-time quantum walk

Spatial search on graphs is one of the most important algorithmic applications quantum walks. To show that a quantum-walk-based more efficient than random-walk-based difficult problem, which has been addressed in several ways. Usually, graph symmetries aid calculation algorithm's computational complexity, and Johnson are an interesting class regarding because they regular, Hamilton-connected, vertex- distance-transitive. In this work, we spatial by continuous-time walk achieves Grover lower bound $\pi\sqrt{N}/2$ with success probability $1$ asymptotically for every fixed diameter, where $N$ number vertices. The proof mathematically rigorous can be used other classes.