{
  "annotation_id": "581fc583-4328-4be3-a9e7-f41e91c85c0a",
  "date_created": "2026-03-02T18:02:17.211000Z",
  "date_modified": "2026-03-02T18:02:17.211000Z",
  "file_hash": "3c2967c4e0956057d992b2bd4f2f4a8e17d328a7ebf57349f9998e5e3ece15d1",
  "private": false,
  "record": {
    "abstract": "Consider a database most of whose entries are marked but the precise fraction\nof marked entries is not known. What is known is that the fraction of marked\nentries is 1-X, where X is a random variable that is uniformly distributed in\nthe range (0,X_0) (X_0 is a small number). The problem is to try to select a\nmarked item from the database in a single query. If the algorithm selects a\nmarked item, it succeeds, else if it selects an unmarked item, it makes an\nerror. How low can we make the probability of error? The best possible\nclassical algorithm can lower the probability of error to O((X_0)^2). The best\nknown quantum algorithms for this problem could also only lower the probability\nof error to O((X_0)^2). Using a recently invented quantum search technique,\nthis paper gives an algorithm that reduces the probability of error to\nO((X_0)^3). The algorithm is asymptotically optimal.",
    "arxiv_id": "quant-ph/0507116",
    "authors": [
      "Lov K. Grover"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum searching amidst uncertainty",
    "url": "https://arxiv.org/abs/quant-ph/0507116"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6c343a0a-cf51-488b-8888-de19ff75d7e8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}