{
  "annotation_id": "91b66f3e-2b50-44d8-be71-54781b73b4e0",
  "date_created": "2026-03-02T18:02:03.635000Z",
  "date_modified": "2026-03-02T18:02:03.635000Z",
  "file_hash": "b91cb539b63c5063c088073d64047b2660334579325e7e4cb50d7c92961c736e",
  "private": false,
  "record": {
    "abstract": "Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for\nelement distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for\nfinding L equal numbers. We point out that this algorithm actually solves a\nmuch more general problem, the problem of finding a subset of size L that\nsatisfies any given property. We review the algorithm and give a considerably\nsimplified analysis of its query complexity. We present several applications,\nincluding two algorithms for the problem of finding an L-clique in an N-vertex\ngraph. One of these algorithms uses O(N^(2L/(L+1))) edge queries, and the other\nuses \\tilde{O}(N^((5L-2)/(2L+4))), which is an improvement for L \u003c= 5. The\nlatter algorithm generalizes a recent result of Magniez, Santha, and Szegedy,\nwho considered the case L=3 (finding a triangle). We also pose two open\nproblems regarding continuous time quantum walk and lower bounds.",
    "arxiv_id": "quant-ph/0311038",
    "authors": [
      "Andrew M. Childs",
      "Jason M. Eisenberg"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.26421/QIC5.7",
    "journal_ref": "Quantum Information and Computation 5, 593 (2005)",
    "title": "Quantum algorithms for subset finding",
    "url": "https://arxiv.org/abs/quant-ph/0311038"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c232a32d-7c38-45b7-9a24-f766efddf4ff",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}