{
  "annotation_id": "ea5c732c-d9e9-4450-940d-ba5c528c420d",
  "date_created": "2026-03-02T18:02:34.186000Z",
  "date_modified": "2026-03-02T18:02:34.186000Z",
  "file_hash": "dd94ed68b8c687e4eb3c1918d4e49b5017bfdb07464d18a122cf8c07d2eb03a7",
  "private": false,
  "record": {
    "abstract": "It has recently been shown that quantum computers can efficiently solve the\nHeisenberg hidden subgroup problem, a problem whose classical query complexity\nis exponential. This quantum algorithm was discovered within the framework of\nusing pretty-good measurements for obtaining optimal measurements in the hidden\nsubgroup problem. Here we show how to solve the Heisenberg hidden subgroup\nproblem using arguments based instead on the symmetry of certain hidden\nsubgroup states. The symmetry we consider leads naturally to a unitary\ntransform known as the Clebsch-Gordan transform over the Heisenberg group. This\ngives a new representation theoretic explanation for the pretty-good\nmeasurement derived algorithm for efficiently solving the Heisenberg hidden\nsubgroup problem and provides evidence that Clebsch-Gordan transforms over\nfinite groups are a new primitive in quantum algorithm design.",
    "arxiv_id": "quant-ph/0612107",
    "authors": [
      "Dave Bacon"
    ],
    "categories": [
      "quant-ph",
      "cs.CC"
    ],
    "title": "How a Clebsch-Gordan Transform Helps to Solve the Heisenberg Hidden   Subgroup Problem",
    "url": "https://arxiv.org/abs/quant-ph/0612107"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7b534902-ba62-4559-9466-25c07efe804a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}