{
  "annotation_id": "e89efaa3-d3a6-419f-b83c-e87c24bbf900",
  "date_created": "2026-03-02T18:02:41.055000Z",
  "date_modified": "2026-03-02T18:02:41.055000Z",
  "file_hash": "70f46687955910f8ab39fed4079ad5cb8308bd1ca886d8fa00310475bee47d23",
  "private": false,
  "record": {
    "abstract": "Grover\u0027s algorithm for quantum searching of a database is generalized to deal\nwith arbitrary initial amplitude distributions. First order linear difference\nequations are found for the time evolution of the amplitudes of the r marked\nand N-r unmarked states. These equations are solved exactly. An expression for\nthe optimal measurement time T \\sim O(\\sqrt{N/r}) is derived which is shown to\ndepend only on the initial average amplitudes of the marked and unmarked\nstates. A bound on the probability of measuring a marked state is derived,\nwhich depends only on the standard deviation of the initial amplitude\ndistributions of the marked or unmarked states.",
    "arxiv_id": "quant-ph/9801066",
    "authors": [
      "David Biron",
      "Ofer Biham",
      "Eli Biham",
      "Markus Grassl",
      "Daniel A. Lidar"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "\"Quantum Computing \u0026 Quantum Communications; First NASA\n  International Conference; selected papers, QCQC\u002798\", C.P. Williams (ed.),\n  Lecture Notes in Computer Science vol. 1509, pp. 140-147 (Springer, 1998).",
    "title": "Generalized Grover Search Algorithm for Arbitrary Initial Amplitude   Distribution",
    "url": "https://arxiv.org/abs/quant-ph/9801066"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "43fd9c26-f072-427d-b962-99492996f339",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}