Continuous‐Time Quantum Walk on the Homogeneous Tree

In this paper, we explore continuous‐time quantum walk on homogeneous tree. By applying the stratification method, we treat vertices in the same stratum of a homogeneous tree as a single vertex and obtain the probability amplitudes for different strata in finite homogeneous tree parts. In particular, when (where denotes the number of strata), we derive the probability amplitudes for each stratum of the homogeneous tree, considering the homogeneous tree's transition from a finite to infinite structure.