  We utilize degenerate perturbation theory to investigate continuous-time
quantum search on second-order truncated simplex lattices. In this work, we
show that the construction of the Hamiltonian must consider the structure of
the lattice. This idea enables effective application of degenerate perturbation
theory to third- and higher-order lattices. We identify two constraints on the
reduction of the dimension of the Hamiltonian. In addition, we elucidate the
influence of the distinct configurations of marked vertices on the quantum
search.
