{
  "annotation_id": "c5136c7c-a2eb-4416-b26d-561c526f7f23",
  "date_created": "2026-03-02T18:02:10.383000Z",
  "date_modified": "2026-03-02T18:02:10.383000Z",
  "file_hash": "07fc2371165d7cb30a3af689b2efca41879d3588b63eec257e0efce67de48290",
  "private": false,
  "record": {
    "abstract": "We exploit Grover operator of database search algorithm for weight decision\nalgorithm. In this research, weight decision problem is to find an exact weight\nw from given two weights as w1 and w2 where w1+w2=1 and 0\u003cw1\u003cw2\u003c1. Firstly, if\na Boolean function is given and when weights are {1/4,3/4}, we can find w with\nonly one application of Grover operator. Secondly, if we apply k many times of\nGrover operator, we can decide w from the set of weights\n{sin^2(\\frac{k}{2k+1}\\frac{\\pi}{2}) cos^2(\\frac{k}{2k+1}\\frac{\\pi}{2})}.\nFinally, by changing the last two Grover operators with two phase conditions,\nwe can decide w from given any set of two weights. To decide w with a sure\nsuccess, if the quantum algorithm requires O(k) Grover steps, then the best\nknown classical algorithm requires \\Omega(k^s) steps where s\u003e2. Hence the\nquantum algorithm achieves at least quadratic speedup.",
    "arxiv_id": "quant-ph/0410043",
    "authors": [
      "Samuel L. Braunstein",
      "Byung-Soo Choi",
      "Subhamoy Maitra",
      "Dibyendu Chakrabarti",
      "Subhroshekhar Ghosh",
      "Partha Mukhopadhyay"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1751-8113/40/29/017",
    "journal_ref": "J. Phys. A: Math. Theor. 40 8441 2007",
    "title": "Quantum algorithm to distinguish Boolean functions of different weights",
    "url": "https://arxiv.org/abs/quant-ph/0410043"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "09fae699-b13a-4417-ad45-57e4ce938d8d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}