Spatial search by continuous-time quantum walk on truncated simplex lattices

Quantum search via continuous-time quantum walk on truncated simplex lattices is an important example of the quantum search on the structured database. In this letter, when the search target is a set of the marked vertices, the run time of the quantum search and the critical jumping rates are derived. Quantum search with the partial information of the location of the marked vertex is also discussed. Furthermore, with the edge weights suitably adjusted, the three-stage search process can be optimized into a two-stage quantum search algorithm on the second-order truncated simplex lattice.