{
  "id": "1312.7646",
  "version": "v1",
  "published": "2013-12-30T07:24:00.000Z",
  "updated": "2013-12-30T07:24:00.000Z",
  "title": "Short random circuits define good quantum error correcting codes",
  "authors": [
    "Winton Brown",
    "Omar Fawzi"
  ],
  "comment": "5 pages",
  "journal": "Proceedings of ISIT 2013, pages 346 - 350",
  "doi": "10.1109/ISIT.2013.6620245",
  "categories": [
    "quant-ph",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \\log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided $\\frac{k}{n} < 1 - \\frac{d}{n} \\log_2 3 - h(\\frac{d}{n})$. In addition, we prove that such circuits typically have a depth of $O( \\log^3 n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-30T07:24:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "E.4",
      "F.1.1"
    ],
    "keywords": [
      "quantum error correcting codes",
      "short random circuits define",
      "random clifford circuits",
      "large rate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.7646B"
    }
  }
}