{
  "annotation_id": "819c1c9f-8ea3-4773-9b4d-110910156bf6",
  "date_created": "2026-03-02T18:02:45.245000Z",
  "date_modified": "2026-03-02T18:02:45.245000Z",
  "file_hash": "9c9adc0de674c31318c04272147d69183692ec4804d7022cdb84730c1c959231",
  "private": false,
  "record": {
    "abstract": "We generalize Grover\u0027s unstructured quantum search algorithm to enable it to\nuse an arbitrary starting superposition and an arbitrary unitary matrix\nsimultaneously. We derive an exact formula for the probability of the\ngeneralized Grover\u0027s algorithm succeeding after n iterations. We show that the\nfully generalized formula reduces to the special cases considered by previous\nauthors. We then use the generalized formula to determine the optimal strategy\nfor using the unstructured quantum search algorithm. On average the optimal\nstrategy is about 12% better than the naive use of Grover\u0027s algorithm. The\nspeedup obtained is not dramatic but it illustrates that a hybrid use of\nquantum computing and classical computing techniques can yield a performance\nthat is better than either alone. We extend the analysis to the case of a\nsociety of k quantum searches acting in parallel. We derive an analytic formula\nthat connects the degree of parallelism with the optimal strategy for\nk-parallel quantum search. We then derive the formula for the expected speed of\nk-parallel quantum search.",
    "arxiv_id": "quant-ph/9904049",
    "authors": [
      "Robert Gingrich",
      "Colin P. Williams",
      "Nicolas Cerf"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.61.052313",
    "journal_ref": "Phys.Rev.A61:052313,2000",
    "title": "Generalized Quantum Search with Parallelism",
    "url": "https://arxiv.org/abs/quant-ph/9904049"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "43e372dc-c090-48fe-9a53-f04e02dfe369",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}