{
  "annotation_id": "9e9adc95-813a-4954-a4d2-492b3cc52a1b",
  "date_created": "2026-03-02T18:02:38.220000Z",
  "date_modified": "2026-03-02T18:02:38.220000Z",
  "file_hash": "d12803c2847885c25e2b772ee41fb2228684f3b37d34994a41d091069b8d881a",
  "private": false,
  "record": {
    "abstract": "We provide a tight analysis of Grover\u0027s recent algorithm for quantum database\nsearching. We give a simple closed-form formula for the probability of success\nafter any given number of iterations of the algorithm. This allows us to\ndetermine the number of iterations necessary to achieve almost certainty of\nfinding the answer. Furthermore, we analyse the behaviour of the algorithm when\nthe element to be found appears more than once in the table and we provide a\nnew algorithm to find such an element even when the number of solutions is not\nknown ahead of time. Using techniques from Shor\u0027s quantum factoring algorithm\nin addition to Grover\u0027s approach, we introduce a new technique for approximate\nquantum counting, which allows to estimate the number of solutions. Finally we\nprovide a lower bound on the efficiency of any possible quantum database\nsearching algorithm and we show that Grover\u0027s algorithm nearly comes within a\nfactor 2 of being optimal in terms of the number of probes required in the\ntable.",
    "arxiv_id": "quant-ph/9605034",
    "authors": [
      "Michel Boyer",
      "Gilles Brassard",
      "Peter Hoeyer",
      "Alain Tapp"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1002/(SICI)1521-3978(199806)46:4/5\u003c493::AID-PROP493\u003e3.0.CO;2-P",
    "journal_ref": "Fortsch.Phys.46:493-506,1998",
    "title": "Tight bounds on quantum searching",
    "url": "https://arxiv.org/abs/quant-ph/9605034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6d23f8b8-4ed7-4582-8e79-9615811510c9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}