{
  "annotation_id": "f053cb52-ed98-4066-842b-946079284f96",
  "date_created": "2026-03-02T18:01:38.869000Z",
  "date_modified": "2026-03-02T18:01:38.869000Z",
  "file_hash": "48712c506512d8bb37a18d622aeb8878c4528b49de6d73f18241fa2d46723d6c",
  "private": false,
  "record": {
    "abstract": "We introduce the concepts of Grover operators and Grover kernels to\nsystematically analyse Grover\u0027s searching algorithms. Then, we investigate a\none-parameter family of quantum searching algorithms of Grover\u0027s type and we\nshow that the standard Grover\u0027s algorithm is a distinguished member of this\nfamily. We show that all the algorithms of this class solve the searching\nproblem with an efficiency of order $O(\\sqrt{N})$, with a coefficient which is\nclass-dependent. The analysis of this dependence is a test of the stability and\nrobustness of the algorithms. We show the stability of this constructions under\nperturbations of the initial conditions and extend them upon a very general\nclass of Grover operators.",
    "arxiv_id": "quant-ph/0009086",
    "authors": [
      "Alberto Galindo",
      "Miguel A. Martin-Delgado"
    ],
    "categories": [
      "quant-ph",
      "cond-mat"
    ],
    "doi": "10.1103/PhysRevA.62.062303",
    "title": "A Family of Grover\u0027s Quantum Searching Algorithms",
    "url": "https://arxiv.org/abs/quant-ph/0009086"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "68f72779-9c81-42cb-9464-1718799a7327",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}