{
  "annotation_id": "ceeb568c-e5b3-4319-8903-dfdd9d17aa37",
  "date_created": "2026-03-02T18:01:45.266000Z",
  "date_modified": "2026-03-02T18:01:45.266000Z",
  "file_hash": "2470fc9a94350b1743c8d3ace9bb4d16a27168a760f6fef1259ecea7ccf15134",
  "private": false,
  "record": {
    "abstract": "We study summation of sequences and integration in the quantum model of\ncomputation. We develop quantum algorithms for computing the mean of sequences\nwhich satisfy a p-summability condition and for integration of functions from\nLebesgue spaces L_p([0,1]^d) and analyze their convergence rates. We also prove\nlower bounds which show that the proposed algorithms are, in many cases,\noptimal within the setting of quantum computing. This extends recent results of\nBrassard, Hoyer, Mosca, and Tapp (2000) on computing the mean for bounded\nsequences and complements results of Novak (2001) on integration of functions\nfrom Hoelder classes.",
    "arxiv_id": "quant-ph/0105116",
    "authors": [
      "Stefan Heinrich"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Summation with an Application to Integration",
    "url": "https://arxiv.org/abs/quant-ph/0105116"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "54c45a53-adb7-430b-9cc4-5bcc1213fecb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}