{
  "annotation_id": "bfb8e1af-f433-4959-853f-45bd334e2f48",
  "date_created": "2026-03-02T18:01:42.182000Z",
  "date_modified": "2026-03-02T18:01:42.182000Z",
  "file_hash": "7f8e81d48fa12403eaed76da9b2c3ed8a5bae7a592d560373fd90653951be5d8",
  "private": false,
  "record": {
    "abstract": "The recursion equation analysis of Grover\u0027s quantum search algorithm\npresented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied\nto the large class of Grover\u0027s type algorithms in which the Hadamard transform\nis replaced by any other unitary transformation and the phase inversion is\nreplaced by a rotation by an arbitrary angle. The time evolution of the\namplitudes of the marked and unmarked states, for any initial complex amplitude\ndistribution is expressed using first order linear difference equations. These\nequations are solved exactly. The solution provides the number of iterations T\nafter which the probability of finding a marked state upon measurement is the\nhighest, as well as the value of this probability, P_max. Both T and P_max are\nfound to depend on the averages and variances of the initial amplitude\ndistributions of the marked and unmarked states, but not on higher moments.",
    "arxiv_id": "quant-ph/0010077",
    "authors": [
      "Eli Biham",
      "Ofer Biham",
      "David Biron",
      "Markus Grassl",
      "Daniel A. Lidar",
      "Daniel Shapira"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.63.012310",
    "journal_ref": "Phys. Rev. A 63, 012310 (2001)",
    "title": "Analysis of Generalized Grover\u0027s Quantum Search Algorithms Using   Recursion Equations",
    "url": "https://arxiv.org/abs/quant-ph/0010077"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3f8cf694-8b3d-472a-9b38-050747f9c625",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}