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 non-isomorphic generalized quadrangles of order $(5^2,5)$ under this matrix and thus provide strongly regular counter-examples to the conjecture.
@article{10_37236_5982,
author = {Chris Godsil and Krystal Guo and Tor G. J. Myklebust},
title = {Quantum walks on generalized quadrangles},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/5982},
zbl = {1373.05105},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5982/}
}
TY - JOUR
AU - Chris Godsil
AU - Krystal Guo
AU - Tor G. J. Myklebust
TI - Quantum walks on generalized quadrangles
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5982/
DO - 10.37236/5982
ID - 10_37236_5982
ER -
%0 Journal Article
%A Chris Godsil
%A Krystal Guo
%A Tor G. J. Myklebust
%T Quantum walks on generalized quadrangles
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5982/
%R 10.37236/5982
%F 10_37236_5982
Chris Godsil; Krystal Guo; Tor G. J. Myklebust. Quantum walks on generalized quadrangles. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/5982
