{
  "annotation_id": "7a630667-0dbf-4163-87cb-5be31abdcbf0",
  "date_created": "2026-03-02T18:02:27.550000Z",
  "date_modified": "2026-03-02T18:02:27.550000Z",
  "file_hash": "b4d8f357360fb9a6a95dfab0373ca3d62253e25335545e5ec243225afda66922",
  "private": false,
  "record": {
    "abstract": "We analyze the connections between the mathematical theory of knots and\nquantum physics by addressing a number of algorithmic questions related to both\nknots and braid groups.\n  Knots can be distinguished by means of `knot invariants\u0027, among which the\nJones polynomial plays a prominent role, since it can be associated with\nobservables in topological quantum field theory.\n  Although the problem of computing the Jones polynomial is intractable in the\nframework of classical complexity theory, it has been recently recognized that\na quantum computer is capable of approximating it in an efficient way. The\nquantum algorithms discussed here represent a breakthrough for quantum\ncomputation, since approximating the Jones polynomial is actually a `universal\nproblem\u0027, namely the hardest problem that a quantum computer can efficiently\nhandle.",
    "arxiv_id": "quant-ph/0606137",
    "authors": [
      "S. Garnerone",
      "A. Marzuoli",
      "M. Rasetti"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1134/S1054660X06110120",
    "journal_ref": "Laser Physics Vol. 16 No. 11 (2006) 1582-1594",
    "title": "Quantum Knitting",
    "url": "https://arxiv.org/abs/quant-ph/0606137"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7beb72dd-7272-48a3-a36a-1af73d427891",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}