{
  "id": "quant-ph/0607203",
  "version": "v1",
  "published": "2006-07-28T09:55:24.000Z",
  "updated": "2006-07-28T09:55:24.000Z",
  "title": "Quantum geometry and quantum algorithms",
  "authors": [
    "S. Garnerone",
    "A. Marzuoli",
    "M. Rasetti"
  ],
  "comment": "Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirardi",
  "journal": "J.Phys.A40:3047-3066,2007",
  "doi": "10.1088/1751-8113/40/12/S10",
  "categories": [
    "quant-ph",
    "gr-qc"
  ],
  "abstract": "Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on the complete solution of Chern-Simons topological quantum field theory and its connection to Wess-Zumino-Witten conformal field theory. The colored Jones polynomial is expressed as the expectation value of the evolution of the q-deformed spin-network quantum automaton. A quantum circuit is constructed capable of simulating the automaton and hence of computing such expectation value. The latter is efficiently approximated using a standard sampling procedure in quantum computation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-28T09:55:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Lx",
      "02.10.Kn",
      "04.60.Nc",
      "04.60.Kz"
    ],
    "keywords": [
      "quantum algorithm",
      "quantum geometry",
      "colored jones polynomial",
      "wess-zumino-witten conformal field theory",
      "chern-simons topological quantum field theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 722770
    }
  }
}