{
  "annotation_id": "b0bf7fd4-5ab5-4267-bef1-89e98727221b",
  "date_created": "2026-03-02T18:01:52.865000Z",
  "date_modified": "2026-03-02T18:01:52.865000Z",
  "file_hash": "da1a126435f871bae6dc427b771fc56e4057977e046ff2588264bef1457f3638",
  "private": false,
  "record": {
    "abstract": "Suppose that a quantum circuit with K elementary gates is known for a unitary\nmatrix U, and assume that U^m is a scalar matrix for some positive integer m.\nWe show that a function of U can be realized on a quantum computer with at most\nO(mK+m^2log m) elementary gates. The functions of U are realized by a generic\nquantum circuit, which has a particularly simple structure. Among other\nresults, we obtain efficient circuits for the fractional Fourier transform.",
    "arxiv_id": "quant-ph/0208130",
    "authors": [
      "Andreas Klappenecker",
      "Martin Roetteler"
    ],
    "categories": [
      "quant-ph",
      "cs.ET"
    ],
    "doi": "10.1103/PhysRevA.67.010302",
    "journal_ref": "Physical Review A, 67, 010302, 2003",
    "title": "Engineering Functional Quantum Algorithms",
    "url": "https://arxiv.org/abs/quant-ph/0208130"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b94ad38b-436a-4d7a-9942-b50fed03553b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}