Quantum Walks on Strongly Regular Graphs

mathematics;combinatorics;graph isomorphism;quantum walk;Combinatorics and Optimization

Guo, Krystal

University of Waterloo

关键词: mathematics;    combinatorics;    graph isomorphism;    quantum walk;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5403/1/Guo_Krystal.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis studies the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We begin by finding the eigenvalues of matrices describing the quantum walk for regular graphs. We also show that if two graphs are isomorphic, then the corresponding matrices produced by the procedure of Emms et al. are cospectral. We then look at the entries of the cube of the transition matrix and find an expression for the matrices produced by the procedure of Emms et al.in terms of the adjacency matrix and incidence matrices of the graph.