{
  "annotation_id": "f8acbc0b-8ff5-4dbf-8e83-39d705627ad2",
  "date_created": "2026-03-02T18:02:16.363000Z",
  "date_modified": "2026-03-02T18:02:16.363000Z",
  "file_hash": "4a6a9b119886167ce7aa171113b2f1b2f9790f0e6b30f77f2ef880363785d798",
  "private": false,
  "record": {
    "abstract": "The hypercomputers compute functions or numbers, or more generally solve\nproblems or carry out tasks, that cannot be computed or solved by a Turing\nmachine. Several numerical simulations of a possible hypercomputational\nalgorithm based on quantum computations previously constructed by the authors\nare presented. The hypercomputability of our algorithm is based on the fact\nthat this algorithm could solve a classically non-computable decision problem,\nHilbert\u0027s tenth problem. The numerical simulations were realized for three\ntypes of Diophantine equations: with and without solutions in non-negative\nintegers, and without solutions by way of various traditional mathematical\npackages.",
    "arxiv_id": "quant-ph/0504021",
    "authors": [
      "Andr\u00e9s Sicard",
      "Juan Ospina",
      "Mario V\u00e9lez"
    ],
    "categories": [
      "quant-ph",
      "cs.LO"
    ],
    "journal_ref": "In \"Adaptive and Natural Computing Algorithms. Proc. of the\n  International Conference in Coimbra, Portugal\". Bernardete Ribeiro et al.\n  (eds.). SpringerWienNewYork, 2005. p. 272--275",
    "title": "Numerical Simulations of a Possible Hypercomputational Quantum Algorithm",
    "url": "https://arxiv.org/abs/quant-ph/0504021"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b6efc91b-e034-4b5a-a03d-d840ae7d09d9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}