{
  "annotation_id": "9a21506d-689a-4176-a1a8-46510dc12933",
  "date_created": "2026-03-02T18:02:48.460000Z",
  "date_modified": "2026-03-02T18:02:48.460000Z",
  "file_hash": "10dbae96b86c036e27c4fd3b01dab38453cf498e21dee7850536f102a0b756da",
  "private": false,
  "record": {
    "abstract": "Clifford algebras are used for definition of spinors. Because of using\nspin-1/2 systems as an adequate model of quantum bit, a relation of the\nalgebras with quantum information science has physical reasons. But there are\nsimple mathematical properties of the algebras those also justifies such\napplications.\n  First, any complex Clifford algebra with 2n generators, Cl(2n,C), has\nrepresentation as algebra of all 2^n x 2^n complex matrices and so includes\nunitary matrix of any quantum n-gate. An arbitrary element of whole algebra\ncorresponds to general form of linear complex transformation. The last property\nis also useful because linear operators are not necessary should be unitary if\nthey used for description of restriction of some unitary operator to subspace.\n  The second advantage is simple algebraic structure of Cl(2n) that can be\nexpressed via tenzor product of standard \"building units\" and similar with\nbehavior of composite quantum systems. The compact notation with 2n generators\nalso can be used in software for modeling of simple quantum circuits by modern\nconventional computers.",
    "arxiv_id": "quant-ph/9907079",
    "authors": [
      "Alexander Yu. Vlasov"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Gates and Clifford Algebras",
    "url": "https://arxiv.org/abs/quant-ph/9907079"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "088141d1-968b-4b20-8a66-939f23dd4520",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}