2023/09/26 by Rohit Sarma Sarkar, Sarkar, Rohit Sarma, Bibhas Adhikari +1
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2309.15194
openalex publication_date 2023/09/26 · openalex created_date 2023/09/30 · openalex updated_date 2026/07/28
In this paper we study discrete-time quantum walks on Cayley graphs corresponding to Dihedral groups, which are graphs with both directed and undirected edges. We consider the walks with coins that are one-parameter continuous deformation of the Grover matrix and can be written as linear combinations of certain permutation matrices. We show that the walks are periodic only for coins that are permutation or negative of a permutation matrix. Finally, we investigate the localization property of the walks through numerical simulations and observe that the walks localize for a wide range of coins for different sizes of the graphs.