{
  "annotation_id": "42eb4e6e-0819-4d4a-a886-abb63c17187d",
  "date_created": "2026-03-02T18:02:20.701000Z",
  "date_modified": "2026-03-02T18:02:20.701000Z",
  "file_hash": "4b99f77bcb96752d55d8069f235f91a5a283d9f1bb96e5dc8205b121c934bed6",
  "private": false,
  "record": {
    "abstract": "We establish essentially optimal bounds on the complexity of initial-value\nproblems in the randomized and quantum settings. For this purpose we define a\nsequence of new algorithms whose error/cost properties improve from step to\nstep. These algorithms yield new upper complexity bounds, which differ from\nknown lower bounds by only an arbitrarily small positive parameter in the\nexponent, and a logarithmic factor. In both the randomized and quantum\nsettings, initial-value problems turn out to be essentially as difficult as\nscalar integration.",
    "arxiv_id": "quant-ph/0510045",
    "authors": [
      "Boleslaw Kacewicz"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Journal of Complexity 22 (2006), 676-690",
    "title": "Almost Optimal Solution of Initial-Value Problems by Randomized and   Quantum Algorithms",
    "url": "https://arxiv.org/abs/quant-ph/0510045"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f8e4aa67-7d72-46b9-8c28-d014354df235",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}