{
  "annotation_id": "33fc7d04-e098-4efb-91a9-3543de7b5890",
  "date_created": "2026-03-02T18:02:37.576000Z",
  "date_modified": "2026-03-02T18:02:37.576000Z",
  "file_hash": "0627e1336e631eeb0fdd4ad4200833913da039776f6ae715cc2c13f9503f57a2",
  "private": false,
  "record": {
    "abstract": "Shor\u0027s algorithms for factorization and discrete logarithms on a quantum\ncomputer employ Fourier transforms preceding a final measurement. It is shown\nthat such a Fourier transform can be carried out in a semi-classical way in\nwhich a ``classical\u0027\u0027 (macroscopic) signal resulting from the measurement of\none bit (embodied in a two-state quantum system) is employed to determine the\ntype of measurement carried out on the next bit, and so forth. In this way the\ntwo-bit gates in the Fourier transform can all be replaced by a smaller number\nof one-bit gates controlled by classical signals. Success in simplifying the\nFourier transform suggests that it may be worthwhile looking for other ways of\nusing semi-classical methods in quantum computing.",
    "arxiv_id": "quant-ph/9511007",
    "authors": [
      "Robert B. Griffiths",
      "Chi-Sheng Niu"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.76.3228",
    "journal_ref": "Phys.Rev.Lett. 76 (1996) 3228-3231",
    "title": "Semiclassical Fourier Transform for Quantum Computation",
    "url": "https://arxiv.org/abs/quant-ph/9511007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bea7e73f-2bb0-4dd6-9181-978a26934916",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}