{
  "id": "1305.5811",
  "version": "v1",
  "published": "2013-05-24T17:44:44.000Z",
  "updated": "2013-05-24T17:44:44.000Z",
  "title": "Complex Hadamard Matrices, Instantaneous Uniform Mixing and Cubes",
  "authors": [
    "Ada Chan"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the continuous-time quantum walks on graphs in the adjacency algebra of the $n$-cube and its related distance regular graphs. For $k\\geq 2$, we find graphs in the adjacency algebra of $(2^{k+2}-8)$-cube that admit instantaneous uniform mixing at time $\\pi/2^k$ and graphs that have perfect state transfer at time $\\pi/2^k$. We characterize the folded $n$-cubes, the halved $n$-cubes and the folded halved $n$-cubes whose adjacency algebra contains a complex Hadamard matrix. We obtain the same conditions for the characterization of these graphs admitting instantaneous uniform mixing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-24T17:44:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex hadamard matrices",
      "admitting instantaneous uniform mixing",
      "continuous-time quantum walks",
      "related distance regular graphs",
      "perfect state transfer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.5811C"
    }
  }
}