{
  "annotation_id": "8338be17-3db7-40db-9550-9bacfa7374e9",
  "date_created": "2026-03-02T18:01:39.160000Z",
  "date_modified": "2026-03-02T18:01:39.160000Z",
  "file_hash": "2bff949a990adb57b91b48df36c06e0ccd699a11f0f539289ff72d1f9238f722",
  "private": false,
  "record": {
    "abstract": "We consider the use of arbitrary phases in quantum amplitude amplification\nwhich is a generalization of quantum searching. We prove that the phase\ncondition in amplitude amplification is given by $\\tan(\\varphi/2) =\n\\tan(\\phi/2)(1-2a)$, where $\\phi$ and $\\phi$ are the phases used and where $a$\nis the success probability of the given algorithm. Thus the choice of phases\ndepends nontrivially and nonlinearly on the success probability. Utilizing this\ncondition, we give methods for constructing quantum algorithms that succeed\nwith certainty and for implementing arbitrary rotations. We also conclude that\nphase errors of order up to $\\frac{1}{\\sqrt{a}}$ can be tolerated in amplitude\namplification.",
    "arxiv_id": "quant-ph/0006031",
    "authors": [
      "Peter Hoyer"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.62.052304",
    "journal_ref": "Phys. Rev. A 62(5), 052304 (5 pp.), Oct 2000",
    "title": "On Arbitrary Phases in Quantum Amplitude Amplification",
    "url": "https://arxiv.org/abs/quant-ph/0006031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a69ff43b-1df0-40a9-ab85-8882d73ab5f5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}