{
  "annotation_id": "ab06866e-6c0e-4b99-892e-8d9b0a153d32",
  "date_created": "2026-03-02T18:01:42.535000Z",
  "date_modified": "2026-03-02T18:01:42.535000Z",
  "file_hash": "dd77e62420b5d4ebef976fb7c179d3ffced686518ea54f13018b32354e5de78c",
  "private": false,
  "record": {
    "abstract": "A problem of universality in simulation of evolution of quantum system and in\ntheory of quantum computations is related with the possibility of expression or\napproximation of arbitrary unitary transformation by composition of specific\nunitary transformations (quantum gates) from given set. In an earlier paper\n(quant-ph/0010071) application of Clifford algebras to constructions of\nuniversal sets of binary quantum gates $U_k \\in U(2^n)$ was shown. For\napplication of a similar approach to non-binary quantum gates $U_k \\in U(l^n)$\nin present work is used rational noncommutative torus ${\\Bbb T}^{2n}_{1/l}$. A\nset of universal non-binary two-gates is presented here as one example.",
    "arxiv_id": "quant-ph/0012009",
    "authors": [
      "Alexander Yu. Vlasov"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.1476391",
    "journal_ref": "J.Math.Phys. 43 (2002) 2959-2964",
    "title": "Noncommutative tori and universal sets of non-binary quantum gates",
    "url": "https://arxiv.org/abs/quant-ph/0012009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "61bd911c-8cbc-4bb0-986b-4a3cd04fbf7a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}