{
  "annotation_id": "4a511aa4-61a9-45e2-b898-ca65f035c79f",
  "date_created": "2026-03-02T18:02:17.042000Z",
  "date_modified": "2026-03-02T18:02:17.042000Z",
  "file_hash": "76a7bcdde7e38364ea7f75171081b4f12be5550129ad6d558ae64db7f44dcd1d",
  "private": false,
  "record": {
    "abstract": "Quantum algorithms may be described by sequences of unitary transformations\ncalled quantum gates and measurements applied to the quantum register of n\nquantum bits, qubits. A collection of quantum gates is called universal if it\ncan be used to construct any n-qubit gate. In 1995, the universality of the set\nof one-qubit gates and controlled NOT gate was shown by Barenco et al. using QR\ndecomposition of unitary matrices. Almost ten years later the decomposition was\nimproved to include essentially fewer elementary gates. In addition, the\ncosine-sine matrix decomposition was applied to efficiently implement\ndecompositions of general quantum gates. In this chapter, we review the\ndifferent types of general gate decompositions and slightly improve the best\nknown gate count for the controlled NOT gates to (23/48)4^n in the leading\norder. In physical realizations, the interaction strength between the qubits\ncan decrease strongly as a function of their distance. Therefore, we also\ndiscuss decompositions with the restriction to nearest-neighbor interactions in\na linear chain of qubits.",
    "arxiv_id": "quant-ph/0504100",
    "authors": [
      "M. Mottonen",
      "J. J. Vartiainen"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Ch. 7 in Trends in Quantum Computing Research (NOVA Publishers,\n  New York), 2006",
    "title": "Decompositions of general quantum gates",
    "url": "https://arxiv.org/abs/quant-ph/0504100"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3ee70a6a-5cae-4996-88c3-3705694bf9a9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}