{
  "annotation_id": "e75efcf3-b8dd-4c2e-8d3a-bfe8f3d54bac",
  "date_created": "2026-03-02T18:01:52.360000Z",
  "date_modified": "2026-03-02T18:01:52.360000Z",
  "file_hash": "2a41c9facc74661979d170efa6e0417b462d7bbf2e86a0f7df9e1b334f53d686",
  "private": false,
  "record": {
    "abstract": "We demonstrate that the unbounded fan-out gate is very powerful.\nConstant-depth polynomial-size quantum circuits with bounded fan-in and\nunbounded fan-out over a fixed basis (denoted by QNCf^0) can approximate with\npolynomially small error the following gates: parity, mod[q], And, Or,\nmajority, threshold[t], exact[q], and Counting. Classically, we need\nlogarithmic depth even if we can use unbounded fan-in gates. If we allow\narbitrary one-qubit gates instead of a fixed basis, then these circuits can\nalso be made exact in log-star depth. Sorting, arithmetical operations, phase\nestimation, and the quantum Fourier transform with arbitrary moduli can also be\napproximated in constant depth.",
    "arxiv_id": "quant-ph/0208043",
    "authors": [
      "Peter Hoyer",
      "Robert Spalek"
    ],
    "categories": [
      "quant-ph",
      "cs.CC"
    ],
    "doi": "10.4086/toc.2005.v001a005",
    "journal_ref": "Theory of Computing, 1(5):81-103, 2005",
    "title": "Quantum Circuits with Unbounded Fan-out",
    "url": "https://arxiv.org/abs/quant-ph/0208043"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "42fae1e7-2a39-4db5-9e9c-ab1ce729134b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}