{
  "annotation_id": "36382292-cfb5-40f6-99c9-ed5d656a645e",
  "date_created": "2026-03-02T18:02:37.286000Z",
  "date_modified": "2026-03-02T18:02:37.286000Z",
  "file_hash": "38c970467035d9f722bf4137fd6a8aa63c65947c587982fbf2ca3804af3c281c",
  "private": false,
  "record": {
    "abstract": "We show that a set of gates that consists of all one-bit quantum gates (U(2))\nand the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x\n\\oplus y)$) is universal in the sense that all unitary operations on\narbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these\ngates. We investigate the number of the above gates required to implement other\ngates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2)\ntransformation to one input bit if and only if the logical AND of all remaining\ninput bits is satisfied. These gates play a central role in many proposed\nconstructions of quantum computational networks. We derive upper and lower\nbounds on the exact number of elementary gates required to build up a variety\nof two-and three-bit quantum gates, the asymptotic number required for $n$-bit\nDeutsch-Toffoli gates, and make some observations about the number required for\narbitrary $n$-bit unitary operations.",
    "arxiv_id": "quant-ph/9503016",
    "authors": [
      "A. Barenco",
      "C. H. Bennett",
      "R. Cleve",
      "D. P. DiVincenzo",
      "N. Margolus",
      "P. Shor",
      "T. Sleator",
      "J. Smolin",
      "H. Weinfurter"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "hep-th"
    ],
    "doi": "10.1103/PhysRevA.52.3457",
    "journal_ref": "Phys.Rev. A52 (1995) 3457",
    "title": "Elementary gates for quantum computation",
    "url": "https://arxiv.org/abs/quant-ph/9503016"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1c2c03ff-15cf-49eb-8ef6-3820420ef70d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}