{
  "annotation_id": "466896c9-f567-4fa3-8e92-766f7fa8a232",
  "date_created": "2026-03-02T18:01:53.168000Z",
  "date_modified": "2026-03-02T18:01:53.168000Z",
  "file_hash": "c8555f0b34692a879ee7e25a592c93811bbba88d9bc768e15d9c0863490b55d4",
  "private": false,
  "record": {
    "abstract": "Here is discussed application of the Weyl pair to construction of universal\nset of quantum gates for high-dimensional quantum system. An application of Lie\nalgebras (Hamiltonians) for construction of universal gates is revisited first.\nIt is shown next, how for quantum computation with qubits can be used\ntwo-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford\nalgebras, and discussed well known applications to product operator formalism\nin NMR, Jordan-Wigner construction in fermionic quantum computations. It is\nintroduced universal set of quantum gates for higher dimensional system\n(``qudit\u0027\u0027), as some generalization of these models. Finally it is briefly\nmentioned possible application of such algebraic methods to design of quantum\nprocessors (programmable gates arrays) and discussed generalization to quantum\ncomputation with continuous variables.",
    "arxiv_id": "quant-ph/0210049",
    "authors": [
      "Alexander Yu. Vlasov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1117/12.517863",
    "journal_ref": "Proc. SPIE 5128, 29 (2003)",
    "title": "Algebras and universal quantum computations with higher dimensional   systems",
    "url": "https://arxiv.org/abs/quant-ph/0210049"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cd311f16-eb92-4efe-82e6-b69f2e21c4f2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}