{
  "annotation_id": "6167f66d-d927-47b9-9dfc-b0cf163221d0",
  "date_created": "2026-03-02T18:02:41.093000Z",
  "date_modified": "2026-03-02T18:02:41.093000Z",
  "file_hash": "92f66d6ae48773c7a0810b9cf10edacba52588b79abe34c1c48ff7bae6884898",
  "private": false,
  "record": {
    "abstract": "We discuss the fundamental role of entanglement as the essential nonclassical\nfeature providing the computational speed-up in the known quantum algorithms.\nWe review the construction of the Fourier transform on an Abelian group and the\nprinciples underlying the fast Fourier transform algorithm. We describe the\nimplementation of the FFT algorithm for the group of integers modulo 2^n in the\nquantum context, showing how the group-theoretic formalism leads to the\nstandard quantum network and identifying the property of entanglement that\ngives rise to the exponential speedup (compared to the classical FFT). Finally\nwe outline the use of the Fourier transform in extracting periodicities, which\nunderlies its utility in the known quantum algorithms.",
    "arxiv_id": "quant-ph/9803072",
    "authors": [
      "Artur Ekert",
      "Richard Jozsa"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1098/rsta.1998.0248",
    "title": "Quantum Algorithms: Entanglement Enhanced Information Processing",
    "url": "https://arxiv.org/abs/quant-ph/9803072"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "757725c9-da89-4d63-8160-c0e579695d55",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}