{
  "annotation_id": "cdcab4e1-c1eb-4571-bbf9-9a719b15dbd0",
  "date_created": "2026-03-02T18:02:16.617000Z",
  "date_modified": "2026-03-02T18:02:16.617000Z",
  "file_hash": "068cc17f968f1617e6c0c8489ec3e0b7670741594ed2aa68802f42836b48e0c8",
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  "record": {
    "abstract": "An algebraic analysis of Grover\u0027s quantum search algorithm is presented for\nthe case in which the initial state is an arbitrary pure quantum state of n\nqubits. This approach reveals the geometrical structure of the quantum search\nprocess, which turns out to be confined to a four-dimensional subspace of the\nHilbert space. This work unifies and generalizes earlier results on the time\nevolution of the amplitudes during the quantum search, the optimal number of\niterations and the success probability. Furthermore, it enables a direct\ngeneralization to the case in which the initial state is a mixed state,\nproviding an exact formula for the success probability.",
    "arxiv_id": "quant-ph/0504149",
    "authors": [
      "D. Shapira",
      "Y. Shimoni",
      "O. Biham"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.042320",
    "journal_ref": "Phys. Rev. A 71, 042320 (2005)",
    "title": "Algebraic analysis of quantum search with pure and mixed states",
    "url": "https://arxiv.org/abs/quant-ph/0504149"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d4b123ae-0ca0-45ed-b3f6-628184972a97",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}