{
  "id": "2202.09080",
  "version": "v1",
  "published": "2022-02-18T08:55:59.000Z",
  "updated": "2022-02-18T08:55:59.000Z",
  "title": "Design for implementation of discrete-time quantum walk with circulant matrix on graph by optical polarizing elements",
  "authors": [
    "Yusuke Mizutani",
    "Etsuo Segawa",
    "Yusuke Higuchi",
    "Leo Matsuoka",
    "Tomoyuki Horikiri"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "In this paper, we introduce a quantum walk whose local scattering at each vertex is denoted by a unitary circulant matrix; namely the circulant quantum walk. We also introduce another quantum walk induced by the circulant quantum walk; namely the optical quantum walk, whose underlying graph is a $2$-regular directed graph and obtained by blowing up the original graph in some way. We propose a design of an optical circuit which implements the stationary state of the optical quantum walk. We show that if the induced optical quantum walk does not have $+1$ eigenvalue, then the stationary state of the optical quantum walk gives that of the original circulant quantum walk. From this result, we give a useful condition for the setting of the circulant quantum walks which can be implemented by this optical circuit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-18T08:55:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete-time quantum walk",
      "optical quantum walk",
      "optical polarizing elements",
      "original circulant quantum walk",
      "implementation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}