{
  "annotation_id": "3d82f012-461e-4033-a613-81c40a5f82a9",
  "date_created": "2026-03-02T18:02:13.516000Z",
  "date_modified": "2026-03-02T18:02:13.516000Z",
  "file_hash": "8ff7d9c2692eb3184cee6b33ef6930f894aff0a130d990cfc9cd78b70260ca25",
  "private": false,
  "record": {
    "abstract": "We resolve the question of whether Fourier sampling can efficiently solve the\nhidden subgroup problem. Specifically, we show that the hidden subgroup problem\nover the symmetric group cannot be efficiently solved by strong Fourier\nsampling, even if one may perform an arbitrary POVM on the coset state. Our\nresults apply to the special case relevant to the Graph Isomorphism problem.",
    "arxiv_id": "quant-ph/0501056",
    "authors": [
      "Cristopher Moore",
      "Alexander Russell",
      "Leonard J. Schulman"
    ],
    "categories": [
      "quant-ph",
      "cs.CC"
    ],
    "title": "The Symmetric Group Defies Strong Fourier Sampling: Part I",
    "url": "https://arxiv.org/abs/quant-ph/0501056"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "52a5fbf9-780c-4957-9886-ff613a6cc519",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}