{
  "annotation_id": "34600f4c-2dcd-4342-9804-4794f1bd2111",
  "date_created": "2026-03-02T18:02:12.968000Z",
  "date_modified": "2026-03-02T18:02:12.968000Z",
  "file_hash": "9a130d64255a9259637127088bce4d186289fe97b6502f52e2acb35b654201b6",
  "private": false,
  "record": {
    "abstract": "We obtain a query lower bound for quantum algorithms solving the phase\nestimation problem. Our analysis generalizes existing lower bound approaches to\nthe case where the oracle Q is given by controlled powers Q^p of Q, as it is\nfor example in Shor\u0027s order finding algorithm. In this setting we will prove a\nlog (1/epsilon) lower bound for the number of applications of Q^p1, Q^p2, ...\nThis bound is tight due to a matching upper bound. We obtain the lower bound\nusing a new technique based on frequency analysis.",
    "arxiv_id": "quant-ph/0412008",
    "authors": [
      "Arvid J. Bessen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.042313",
    "journal_ref": "Phys. Rev. A 71, 042313 (2005)",
    "title": "A Lower Bound for Quantum Phase Estimation",
    "url": "https://arxiv.org/abs/quant-ph/0412008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0de890a7-8f91-46d5-b35d-1e774b80d67c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}