{
  "annotation_id": "0044a860-593e-4615-8978-c7d398050833",
  "date_created": "2026-03-02T18:01:45.524000Z",
  "date_modified": "2026-03-02T18:01:45.524000Z",
  "file_hash": "45d4c7f9f029dfb9a8b7aaa5f6feaeed7007cef283b53545faef4839551b863a",
  "private": false,
  "record": {
    "abstract": "In standard Grover\u0027s algorithm for quantum searching, the probability of\nfinding the marked item is not exactly 1. In this Letter we present a modified\nversion of Grover\u0027s algorithm that searches a marked state with full successful\nrate. The modification is done by replacing the phase inversion by two phase\nrotation through angle $\\phi$. The rotation angle is given analytically to be\n$\\phi=2 \\arcsin(\\sin{\\pi\\over (4J+6)}\\over \\sin\\beta)$, where\n$\\sin\\beta={1\\over \\sqrt{N}}$, $N$ the number of items in the database, and $J$\nan integer equal to or greater than the integer part of $({\\pi\\over\n2}-\\beta)/(2\\beta)$. Upon measurement at $(J+1)$-th iteration, the marked state\nis obtained with certainty.",
    "arxiv_id": "quant-ph/0106071",
    "authors": [
      "G. L. Long"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.64.022307",
    "journal_ref": "Phys. Rev. A64 (2001) 022307",
    "title": "Grover Algorithm with zero theoretical failure rate",
    "url": "https://arxiv.org/abs/quant-ph/0106071"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eed64e66-31e8-4ae8-90f6-38f6eae84282",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}