{
  "annotation_id": "d107c61f-307f-4399-a2ca-72c9e616e3a9",
  "date_created": "2026-03-02T18:02:27.608000Z",
  "date_modified": "2026-03-02T18:02:27.608000Z",
  "file_hash": "0aad0c1c8fa6ca040fbf7bcde69ae9f652784947b1d830f7a777a8cc4493c177",
  "private": false,
  "record": {
    "abstract": "We construct a quantum algorithm to approximate efficiently the colored Jones\npolynomial of the plat presentation of any oriented link L at a fixed root of\nunity q. Our construction is based on SU(2) Chern-Simons topological quantum\nfield theory (and associated Wess-Zumino-Witten conformal field theory) and\nexploits the q-deformed spin network as computational background.\n  As proved in (S. Garnerone, A. Marzuoli, M. Rasetti, quant-ph/0601169), the\ncolored Jones polynomial can be evaluated in a number of elementary steps,\nbounded from above by a linear function of the number of crossings of the link,\nand polynomially bounded with respect to the number of link strands. Here we\nshow that the Kaul unitary representation of colored oriented braids used there\ncan be efficiently approximated on a standard quantum circuit.",
    "arxiv_id": "quant-ph/0606167",
    "authors": [
      "S. Garnerone",
      "A. Marzuoli",
      "M. Rasetti"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An efficient quantum algorithm for colored Jones polynomials",
    "url": "https://arxiv.org/abs/quant-ph/0606167"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b08f98ea-7824-444d-977d-acfec845cf90",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}