Quantum Walks on Generalized Quadrangles

  • Chris Godsil
  • Krystal Guo
  • Tor G. J. Myklebust
Keywords: Algebraic Graph Theory, Quantum Walks, Graph Isomorphism


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.
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