Quantum Walks on Generalized Quadrangles [article]

Chris Godsil, Krystal Guo, Tor G.J. Myklebust
2015 arXiv   pre-print
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.
arXiv:1511.01962v1 fatcat:yyiwglakvfbijgcfidlyluzxwu