{
  "id": "1511.01962",
  "version": "v1",
  "published": "2015-11-06T00:51:58.000Z",
  "updated": "2015-11-06T00:51:58.000Z",
  "title": "Quantum Walks on Generalized Quadrangles",
  "authors": [
    "Chris Godsil",
    "Krystal Guo",
    "Tor G. J. Myklebust"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO",
    "quant-ph"
  ],
  "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 non-isomorphic generalized quadrangles of order $(5^2,5)$ under this matrix and thus provide strongly regular counter-examples to the conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-06T00:51:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "81P68"
    ],
    "keywords": [
      "quantum walk",
      "line intersection graphs",
      "distinguishes strongly regular graphs",
      "transition matrix",
      "non-isomorphic generalized quadrangles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151101962G"
    }
  }
}