{
  "annotation_id": "1ab3449f-8284-4aad-91c9-a6a7bddd8bbe",
  "date_created": "2026-03-02T18:01:45.334000Z",
  "date_modified": "2026-03-02T18:01:45.334000Z",
  "file_hash": "e7e67babb7ac6feb3d731607d8f0270a4733d03f5e2bcd004ce7d83025be5d72",
  "private": false,
  "record": {
    "abstract": "In this paper we derived the precise formula in a sine function form of the\nnorm of the amplitude in the desired state, and by means of he precise formula\nwe presented the necessary and sufficient phase condition for any quantum\nalgorithm with arbitrary phase rotations. We also showed that the phase\ncondition: identical rotation angles, is a sufficient but not a necessary phase\ncondition.",
    "arxiv_id": "quant-ph/0107010",
    "authors": [
      "Dafa Li"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s11232-005-0159-x",
    "journal_ref": "The revised version was published in TMPH(theoretical and\n  methematical physics): vol 144 (3) 1279-1287(2005).",
    "title": "The Precise Formula in a Sine Function Form of the norm of the Amplitude   and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm   with Arbitrary Phase Rotations",
    "url": "https://arxiv.org/abs/quant-ph/0107010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5a3a0693-c8be-49d4-bb67-34832634094b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}