{
  "annotation_id": "38e691c7-802d-4fd3-9634-0437b4357488",
  "date_created": "2026-03-02T18:02:41.302000Z",
  "date_modified": "2026-03-02T18:02:41.302000Z",
  "file_hash": "1d7422b8c51c1a081c5a2c3a0596b17dc0c8b30ef800f9322ed8968d03b6cbec",
  "private": false,
  "record": {
    "abstract": "Consider a function f which is defined on the integers from 1 to N and takes\nthe values -1 and +1. The parity of f is the product over all x from 1 to N of\nf(x). With no further information about f, to classically determine the parity\nof f requires N calls of the function f. We show that any quantum algorithm\ncapable of determining the parity of f contains at least N/2 applications of\nthe unitary operator which evaluates f. Thus for this problem, quantum\ncomputers cannot outperform classical computers.",
    "arxiv_id": "quant-ph/9802045",
    "authors": [
      "E. Farhi",
      "J. Goldstone",
      "S. Gutmann",
      "M. Sipser"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.81.5442",
    "journal_ref": "Phys.Rev.Lett.81:5442-5444,1998",
    "title": "A Limit on the Speed of Quantum Computation in Determining Parity",
    "url": "https://arxiv.org/abs/quant-ph/9802045"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "90954c05-fde5-4656-afa9-02fa79e82ea3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}