Quantum Walks on Generalized Quadrangles
Abstract
We study 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 $S^+(U^3)$, a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We probabilistically compute the spectrum of the line intersection graphs of two nonisomorphic generalized quadrangles of order $(5^2,5)$ under this matrix and thus provide strongly regular counterexamples to the conjecture.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.01962
 Bibcode:
 2015arXiv151101962G
 Keywords:

 Mathematics  Combinatorics;
 Quantum Physics;
 05C50;
 81P68
 EPrint:
 5 pages