{
  "annotation_id": "e7c3875e-0f58-440e-a9d9-9b2d17a624a6",
  "date_created": "2026-03-02T18:02:15.896000Z",
  "date_modified": "2026-03-02T18:02:15.896000Z",
  "file_hash": "0a10c5f14189d7296870747509ec5d254918d320678af2b207715caa49084128",
  "private": false,
  "record": {
    "abstract": "In this paper, we analyze the quantum counting under the decoherence, which\ncan find the number of solutions satisfying a given oracle. We investigate\nprobability distributions related to the first order term of the error rate on\nthe quantum counting with the depolarizing channel. We also implement two\ncircuits for the quantum counting -- the ascending-order circuit and the\ndescending-order circuit -- by reversing ordering of application of\ncontrolled-Grover operations. By theoretical and numerical calculations for\nprobability distributions, we reveal the difference of probability\ndistributions on two circuits in the presence of decoherence and show that the\nascending-order circuit is more robust against the decoherence than the\ndescending-order circuit. This property of the robustness is applicable to the\nphase estimation such as the factoring.",
    "arxiv_id": "quant-ph/0503202",
    "authors": [
      "Jun Hasegawa",
      "Fumitaka Yura"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Theoretical Analyses of Quantum Counting against Decoherence Errors",
    "url": "https://arxiv.org/abs/quant-ph/0503202"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5bb19510-cd58-4560-a4da-b8e07db61f89",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}