Quantum walks on a network based on a dual Sierpinski gasket and a dendrimer
Phys. Rev. A 112, 012225 – Published 28 July, 2025
DOI: https://doi.org/10.1103/v78n-y49t
Abstract
We investigate the transport properties of quantum walks on a multihierarchical network which is built by a replication of the dual Sierpinski gasket in the form of a regular dendrimer. The efficiency of the transport is monitored through the exact and the average return probabilities, which are obtained by implementing a continuous-time quantum walk (CTQW) model. All these probabilities (classical and quantum) are determined by knowing the eigenvalues and eigenvectors of the connectivity matrix. For our networks the complete eigenvalue spectrum is determined iteratively, a process that facilitates the analysis of very large networks. The classical return probability can be separated into two distinct components which depend on the underlying topologies: the dual Sierpinski gasket and the dendrimer. The quantum walks show strong localization effects, which are more accentuated when the starting node is peripheral. The quantum long-time average probability is determined analytically, depending solely on the generation numbers of our fractal and dendrimer. For networks with generation number of dual Sierpinski gasket higher than 5 the long-time probability keeps the same and depends only on the spectral dimension of the fractal.
