{
  "id": "1610.00547",
  "version": "v1",
  "published": "2016-10-03T13:39:39.000Z",
  "updated": "2016-10-03T13:39:39.000Z",
  "title": "Criteria for universality of quantum gates",
  "authors": [
    "Adam Sawicki",
    "Katarzyna Karnas"
  ],
  "comment": "5 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.GR",
    "math.MP"
  ],
  "abstract": "We consider the problem of deciding if a set of quantum one-qudit gates $\\mathcal{S}=\\{U_1,\\ldots,U_n\\}$ is universal. We provide compact form criteria that involve spectra of the gates and linear equations whose coefficients are polynomial in entries of the gates and their complex conjugates. Moreover, for non-universal $\\mathcal{S}$ our criteria indicate what type of gates can be added to $\\mathcal{S}$ to turn it into a universal set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-03T13:39:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum gates",
      "universality",
      "quantum one-qudit gates",
      "compact form criteria",
      "universal set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}