{
  "annotation_id": "586276d0-b52a-40d6-87c4-a99e89a91d47",
  "date_created": "2026-03-02T18:02:27.507000Z",
  "date_modified": "2026-03-02T18:02:27.507000Z",
  "file_hash": "117e99c2cf07baba9fbcc4314bbebb95dde9ddadabf0b6fe32db6806460cba39",
  "private": false,
  "record": {
    "abstract": "We review the q-deformed spin network approach to Topological Quantum Field\nTheory and apply these methods to produce unitary representations of the braid\ngroups that are dense in the unitary groups. Our methods are rooted in the\nbracket state sum model for the Jones polynomial. We give our results for a\nlarge class of representations based on values for the bracket polynomial that\nare roots of unity. We make a separate and self-contained study of the quantum\nuniversal Fibonacci model in this framework. We apply our results to give\nquantum algorithms for the computation of the colored Jones polynomials for\nknots and links, and the Witten-Reshetikhin-Turaev invariant of three\nmanifolds.",
    "arxiv_id": "quant-ph/0606114",
    "authors": [
      "Louis H. Kauffman",
      "Samuel J. Lomonaco Jr"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "$q$ - Deformed Spin Networks, Knot Polynomials and Anyonic Topological   Quantum Computation",
    "url": "https://arxiv.org/abs/quant-ph/0606114"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "abce54bf-2082-45b0-a994-7161d8576839",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}