{
  "annotation_id": "8a41b4a5-ea6a-4b65-a5de-b6c3778b4b4d",
  "date_created": "2026-03-02T18:02:24.030000Z",
  "date_modified": "2026-03-02T18:02:24.030000Z",
  "file_hash": "054e08dde7834ff88bfc6fa8b21b4e40a46265c5562c94805ba90d18ddedd669",
  "private": false,
  "record": {
    "abstract": "We study a set of truncated matrices, given by Smith~\\cite{Smith2005}, in\nconnection to an identification criterion for the ground state in our proposed\nquantum adiabatic algorithm for Hilbert\u0027s tenth problem. We identify the origin\nof the trouble for this truncated example and show that for a suitable choice\nof some parameter it can always be removed. We also argue that it is only an\nartefact of the truncation of the underlying Hilbert spaces, through showing\nits sensitivity to different boundary conditions available for such a\ntruncation. It is maintained that the criterion, in general, should be\napplicable provided certain conditions are satisfied. We also point out that,\napart from this one, other criteria serving the same identification purpose may\nalso be available.",
    "arxiv_id": "quant-ph/0602145",
    "authors": [
      "Tien D. Kieu"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the identification of the ground state based on occupation   probabilities: An investigation of Smith\u0027s apparent counterexamples",
    "url": "https://arxiv.org/abs/quant-ph/0602145"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "330bb498-a022-47b8-9f84-e3a5946ef8ff",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}