{
  "annotation_id": "73da7c83-ba17-4848-80d6-78666d539e98",
  "date_created": "2026-03-02T18:01:46.119000Z",
  "date_modified": "2026-03-02T18:01:46.119000Z",
  "file_hash": "ddd4f1221d4a374833efd4f36904a204a96eb67e3fcd2688d4f2c73f8753ea81",
  "private": false,
  "record": {
    "abstract": "Quantum compiling addresses the problem of approximating an arbitrary quantum\ngate with a string of gates drawn from a particular finite set. It has been\nshown that this is possible for almost all choices of base sets and furthermore\nthat the number of gates required for precision epsilon is only polynomial in\nlog 1/epsilon. Here we prove that using certain sets of base gates quantum\ncompiling requires a string length that is linear in log 1/epsilon, a result\nwhich matches the lower bound from counting volume up to constant factor.",
    "arxiv_id": "quant-ph/0111031",
    "authors": [
      "Aram W. Harrow",
      "Benjamin Recht",
      "Isaac L. Chuang"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1495899",
    "journal_ref": "J. Math. Phys. 43, 4445 (2002)",
    "title": "Efficient Discrete Approximations of Quantum Gates",
    "url": "https://arxiv.org/abs/quant-ph/0111031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c61eb711-7045-45ac-b0ac-1a5061d2f92d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}