{
  "annotation_id": "97e1efbf-8aa0-4dd2-928b-ce2fb2a3a495",
  "date_created": "2026-03-02T18:01:39.102000Z",
  "date_modified": "2026-03-02T18:01:39.102000Z",
  "file_hash": "caa6812d10eb814e68f0c30a48e97e30f10c263f6ce04f1e4a783c4e16669bd4",
  "private": false,
  "record": {
    "abstract": "It is known that quantum computers yield a speed-up for certain discrete\nproblems. Here we want to know whether quantum computers are useful for\ncontinuous problems. We study the computation of the integral of functions from\nthe classical Hoelder classes with d variables. The optimal orders for the\ncomplexity of deterministic and (general) randomized methods are known. We\nobtain the respective optimal orders for quantum algorithms and also for\nrestricted Monte Carlo (only coin tossing instead of general random numbers).\nTo summarize the results one can say that (1) there is an exponential speed-up\nof quantum algorithms over deterministic (classical) algorithms, if the\nsmoothness is small; (2) there is a (roughly) quadratic speed-up of quantum\nalgorithms over randomized classical methods, if the smoothness is small.",
    "arxiv_id": "quant-ph/0008124",
    "authors": [
      "Erich Novak"
    ],
    "categories": [
      "quant-ph",
      "math.NA"
    ],
    "journal_ref": "Journal of Complexity, 17 (2001), 2-16",
    "title": "Quantum Complexity of Integration",
    "url": "https://arxiv.org/abs/quant-ph/0008124"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0ab0ebc2-553b-4c9e-9127-00a4b9c820b5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}