{
  "annotation_id": "b5cb2092-1ce0-4252-8b47-2dd1d00dee6e",
  "date_created": "2026-03-02T18:02:44.845000Z",
  "date_modified": "2026-03-02T18:02:44.845000Z",
  "file_hash": "11f62cd9acea79c09064b04cda69ad37bcb9dd360188d673475ceadcc40f3541",
  "private": false,
  "record": {
    "abstract": "It is well known that quantum computers can efficiently find a hidden\nsubgroup $H$ of a finite Abelian group $G$. This implies that after only a\npolynomial (in $\\log |G|$) number of calls to the oracle function, the states\ncorresponding to different candidate subgroups have exponentially small inner\nproduct. We show that this is true for noncommutative groups also. We present a\nquantum algorithm which identifies a hidden subgroup of an arbitrary finite\ngroup $G$ in only a linear (in $\\log |G|$) number of calls to the oracle\nfunction. This is exponentially better than the best classical algorithm.\nHowever our quantum algorithm requires an exponential amount of time, as in the\nclassical case.",
    "arxiv_id": "quant-ph/9901034",
    "authors": [
      "Mark Ettinger",
      "Peter Hoyer",
      "Emanuel Knill"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Hidden Subgroup States are Almost Orthogonal",
    "url": "https://arxiv.org/abs/quant-ph/9901034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4e1be3d1-c9ca-417f-a725-c4f745fce2ae",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}