{
  "annotation_id": "e4a8102f-167f-4285-8a21-45d33dd05f66",
  "date_created": "2026-03-02T18:02:44.589000Z",
  "date_modified": "2026-03-02T18:02:44.589000Z",
  "file_hash": "c0e09d6b8e0c6aa7847e791e4004ebb71961c807eda6cabe48dfb761afc8293c",
  "private": false,
  "record": {
    "abstract": "Quantum algorithms for factoring and discrete logarithm have previously been\ngeneralized to finding hidden subgroups of finite Abelian groups. This paper\nexplores the possibility of extending this general viewpoint to finding hidden\nsubgroups of noncommutative groups. We present a quantum algorithm for the\nspecial case of dihedral groups which determines the hidden subgroup in a\nlinear number of calls to the input function. We also explore the difficulties\nof developing an algorithm to process the data to explicitly calculate a\ngenerating set for the subgroup. A general framework for the noncommutative\nhidden subgroup problem is discussed and we indicate future research\ndirections.",
    "arxiv_id": "quant-ph/9807029",
    "authors": [
      "Mark Ettinger",
      "Peter Hoyer"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/3-540-49116-3_45",
    "journal_ref": "Proceedings of 16th Annual Symposium on Theoretical Aspects of\n  Computer Science (STACS), Trier, Germany, pp. 478-487, 1999",
    "title": "On Quantum Algorithms for Noncommutative Hidden Subgroups",
    "url": "https://arxiv.org/abs/quant-ph/9807029"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b9abc4c5-c248-4968-84c7-b6707ebc03a9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}