Perfect state transfer in Grover walks on association schemes and distance-regular graphs
Combinatorics
2025-06-23 v2 Quantum Physics
Abstract
This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association scheme. Our focus includes specific association schemes, namely the Hamming and Johnson schemes. We characterize all graphs on the classes of Hamming and Johnson schemes that exhibit perfect state transfer. Furthermore, we study perfect state transfer on distance-regular graphs. We provide complete characterizations for exhibiting perfect state transfer on distance-regular graphs of diameter and diameter , as well as integral distance-regular graphs.
Keywords
Cite
@article{arxiv.2506.07439,
title = {Perfect state transfer in Grover walks on association schemes and distance-regular graphs},
author = {Koushik Bhakta and Bikash Bhattacharjya},
journal= {arXiv preprint arXiv:2506.07439},
year = {2025}
}