{
  "annotation_id": "a50b0e3c-54f8-4c39-9100-288298a7c735",
  "date_created": "2026-03-02T18:02:44.351000Z",
  "date_modified": "2026-03-02T18:02:44.351000Z",
  "file_hash": "5dd18328e17f2eb844ba5caee8bb9b3fafc79ba2d357ff29ac10e6584df70be1",
  "private": false,
  "record": {
    "abstract": "Grover\u0027s algorithm for quantum searching is generalized to deal with\narbitrary initial complex amplitude distributions. First order linear\ndifference equations are found for the time evolution of the amplitudes of the\nmarked and unmarked states. These equations are solved exactly. New expressions\nare derived for the optimal time of measurement and the maximal probability of\nsuccess. They are found to depend on the averages and variances of the initial\namplitude distributions of the marked and unmarked states, but not on higher\nmoments. Our results imply that Grover\u0027s algorithm is robust against modest\nnoise in the amplitude initialization procedure.",
    "arxiv_id": "quant-ph/9807027",
    "authors": [
      "Eli Biham",
      "Ofer Biham",
      "David Biron",
      "Markus Grassl",
      "Daniel A. Lidar"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.60.2742",
    "journal_ref": "Phys.Rev. A60 (1999) 2742",
    "title": "Grover\u0027s Quantum Search Algorithm for an Arbitrary Initial Amplitude   Distribution",
    "url": "https://arxiv.org/abs/quant-ph/9807027"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ac7b2ccc-278e-4fc0-9bc9-15bdc4ec83b7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}