{
  "annotation_id": "c70007d6-3609-4502-90eb-df7ba75f88c9",
  "date_created": "2026-03-02T18:02:45.244000Z",
  "date_modified": "2026-03-02T18:02:45.244000Z",
  "file_hash": "dd65b5f8e18398c91433cc35f94d0d5d82625eca4f6531714f9f4788ca7c9e33",
  "private": false,
  "record": {
    "abstract": "We show that Durr-Hoyer\u0027s quantum algorithm of searching for extreme point of\ninteger function can not be sped up for functions chosen randomly. Any other\nalgorithm acting in substantially shorter time $o(\\sqrt{2^n})$ gives incorrect\nanswer for the functions with the single point of maximum chosen randomly with\nprobability converging to 1. The lower bound as $\\Omega (\\sqrt{2^n /b})$ was\nestablished for the quantum search for solution of equations $f(x)=1$ where $f$\nis a Boolean function with $b$ such solutions chosen at random with probability\nconverging to 1.",
    "arxiv_id": "quant-ph/9806001",
    "authors": [
      "Yuri Ozhigov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1098/rspa.1999.0397",
    "journal_ref": "Proc.Roy.Soc.Lond. A455 (1999) 2165-2172",
    "title": "Lower Bounds of Quantum Search for Extreme Point",
    "url": "https://arxiv.org/abs/quant-ph/9806001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "29938875-7926-40c0-97c5-21fa0eaa9488",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}