{
  "annotation_id": "c712318b-a16c-44fd-8a5f-e44c29e30fa6",
  "date_created": "2026-03-02T18:02:03.180000Z",
  "date_modified": "2026-03-02T18:02:03.180000Z",
  "file_hash": "147bbd40fa876bcf1fe9b5d27cffdbd188b1562f5c3869b6f5129f9ce4015401",
  "private": false,
  "record": {
    "abstract": "We review the proposal of a quantum algorithm for Hilbert\u0027s tenth problem and\nprovide further arguments towards the proof that: (i) the algorithm terminates\nafter a finite time for any input of Diophantine equation; (ii) the final\nground state which contains the answer for the Diophantine equation can be\nidentified as the component state having better-than-even probability to be\nfound by measurement at the end time--even though probability for the final\nground state in a quantum adiabatic process need not monotonically increase\ntowards one in general. Presented finally are the reasons why our algorithm is\noutside the jurisdiction of no-go arguments previously employed to show that\nHilbert\u0027s tenth problem is recursively non-computable.",
    "arxiv_id": "quant-ph/0310052",
    "authors": [
      "Tien D. Kieu"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum adiabatic algorithm for Hilbert\u0027s tenth problem: I. The   algorithm",
    "url": "https://arxiv.org/abs/quant-ph/0310052"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5cf33d92-6115-42cf-9445-7dd25dc77023",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}