{
  "annotation_id": "a4a9a339-8093-4ee5-a7fa-d80858ffbcc1",
  "date_created": "2026-03-02T18:02:13.629000Z",
  "date_modified": "2026-03-02T18:02:13.629000Z",
  "file_hash": "2d4faa220cc457bc5ef09b0ec4130b39bbe3bb61dee9f2f10419a145879e5faa",
  "private": false,
  "record": {
    "abstract": "We present a simple method for constructing optimal fault-tolerant\napproximations of arbitrary unitary gates using an arbitrary discrete universal\ngate set. The method presented is numerical and scales exponentially with the\nnumber of gates used in the approximation. However, for the specific case of\narbitrary single-qubit gates and the fault-tolerant gates permitted by the\nconcatenated 7-qubit Steane code, we find gate sequences sufficiently long and\naccurate to permit the fault-tolerant factoring of numbers thousands of bits\nlong. A general scaling law of how rapidly these fault-tolerant approximations\nconverge to arbitrary single-qubit gates is also determined.",
    "arxiv_id": "quant-ph/0411206",
    "authors": [
      "Austin G. Fowler"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Quantum Information and Computation 11, 867-873 (2011)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Constructing arbitrary Steane code single logical qubit fault-tolerant   gates",
    "url": "https://arxiv.org/abs/quant-ph/0411206"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "53251d30-db58-434c-b8de-3d6d5cc3cbf7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}