{
  "annotation_id": "aa0120d4-d52a-4dd2-9fa3-4035c060df7a",
  "date_created": "2026-03-02T18:02:10.164000Z",
  "date_modified": "2026-03-02T18:02:10.164000Z",
  "file_hash": "5b6408527bfb3bb00ad35b95c4870d5347d2de6ac7aa35f80d37a4fd39197d96",
  "private": false,
  "record": {
    "abstract": "The Schur basis on n d-dimensional quantum systems is a generalization of the\ntotal angular momentum basis that is useful for exploiting symmetry under\npermutations or collective unitary rotations. We present efficient (size\npoly(n,d,log(1/\\epsilon)) for accuracy \\epsilon) quantum circuits for the Schur\ntransform, which is the change of basis between the computational and the Schur\nbases. These circuits are based on efficient circuits for the Clebsch-Gordan\ntransformation. We also present an efficient circuit for a limited version of\nthe Schur transform in which one needs only to project onto different Schur\nsubspaces. This second circuit is based on a generalization of phase estimation\nto any nonabelian finite group for which there exists a fast quantum Fourier\ntransform.",
    "arxiv_id": "quant-ph/0407082",
    "authors": [
      "Dave Bacon",
      "Isaac Chuang",
      "Aram Harrow"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.97.170502",
    "journal_ref": "Phys. Rev. Lett., Vol. 97, 170502 (2006)",
    "title": "Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms",
    "url": "https://arxiv.org/abs/quant-ph/0407082"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "460ec7e1-e0d0-42ec-bada-8877b58f9067",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}