{
  "annotation_id": "8bad2b94-c3d9-4894-8ebe-8921c5deb72c",
  "date_created": "2026-03-02T18:02:48.583000Z",
  "date_modified": "2026-03-02T18:02:48.583000Z",
  "file_hash": "5c99f211b4269532890ef7f4199cc86d25b97b253bee61ece65316ab4d33b618",
  "private": false,
  "record": {
    "abstract": "We present a quantum version of the classical probabilistic algorithms\n$\\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of\nGrover\u0027s operator for the quantum search of a database and of Shor\u0027s Fourier\ntransform for extracting the periodicity of a function, and their combined use\nin the counting algorithm originally introduced by Brassard et al. One of the\nmain features of our quantum probabilistic algorithm is its full unitarity and\nreversibility, which would make its use possible as part of larger and more\ncomplicated networks in quantum computers. As an example of this we describe\npolynomial time algorithms for studying some important problems in number\ntheory, such as the test of the primality of an integer, the so called \u0027prime\nnumber theorem\u0027 and Hardy and Littlewood\u0027s conjecture about the asymptotic\nnumber of representations of an even integer as a sum of two primes.",
    "arxiv_id": "quant-ph/9907020",
    "authors": [
      "A. Carlini",
      "A. Hosoya"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.62.032312",
    "title": "Quantum Probabilistic Subroutines and Problems in Number Theory",
    "url": "https://arxiv.org/abs/quant-ph/9907020"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0d9b8b00-eee0-4a87-9bd1-ab71a791abae",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}