{
  "annotation_id": "3120edd6-80d0-4a85-a035-4f561efbe478",
  "date_created": "2026-03-02T18:02:40.454000Z",
  "date_modified": "2026-03-02T18:02:40.454000Z",
  "file_hash": "c8e3b0f49d065b6e9b862b0d7765566793471fe7d4962d770915ae1092c8ea3f",
  "private": false,
  "record": {
    "abstract": "Quantum mechanics requires the operation of quantum computers to be unitary,\nand thus makes it important to have general techniques for developing fast\nquantum algorithms for computing unitary transforms. A quantum routine for\ncomputing a generalized Kronecker product is given. Applications include\nre-development of the networks for computing the Walsh-Hadamard and the quantum\nFourier transform. New networks for two wavelet transforms are given. Quantum\ncomputation of Fourier transforms for non-Abelian groups is defined. A slightly\nrelaxed definition is shown to simplify the analysis and the networks that\ncomputes the transforms. Efficient networks for computing such transforms for a\nclass of metacyclic groups are introduced. A novel network for computing a\nFourier transform for a group used in quantum error-correction is also given.",
    "arxiv_id": "quant-ph/9702028",
    "authors": [
      "Peter Hoyer"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Efficient Quantum Transforms",
    "url": "https://arxiv.org/abs/quant-ph/9702028"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "393e9c5e-e755-48ce-b6b2-054241b8ca05",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}