{
  "annotation_id": "1e8331a3-d79e-47dc-bfab-fe06ed54cc13",
  "date_created": "2026-03-02T18:02:47.654000Z",
  "date_modified": "2026-03-02T18:02:47.654000Z",
  "file_hash": "9c8db6d8bdd4cc29330de980a0a2f1a42c533e67850f42949b54d28077dd79cc",
  "private": false,
  "record": {
    "abstract": "Each iteration in Grover\u0027s original quantum search algorithm contains 4\nsteps: two Hadamard-Walsh transformations and two amplitudes inversions. When\nthe inversion of the marked state is replaced by arbitrary phase rotation\n\\theta and the inversion for the prepared state |\\gamma\u003e is replaced by\nrotation through \\phi, we found that these phase rotations must satisfy a\nmatching condition \\theta=\\phi. Approximate formula for the amplitude of the\nmarked state after an arbitrary number of iterations are also derived. We give\nalso a simple explanation of the phase matching requirement.",
    "arxiv_id": "quant-ph/9906020",
    "authors": [
      "Gui Lu Long",
      "Yan Song Li",
      "Wei Lin Zhang",
      "Li Niu"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0375-9601(99)00631-3",
    "journal_ref": "Phys.Lett. A262 (1999) 27-34",
    "title": "Phase matching in quantum searching",
    "url": "https://arxiv.org/abs/quant-ph/9906020"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "41b7652f-9e49-4b0a-85c2-4b4c93d3ac83",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}