{
  "annotation_id": "86432ef9-ecd5-4aa9-9fc0-c382938d1936",
  "date_created": "2026-03-02T18:02:13.461000Z",
  "date_modified": "2026-03-02T18:02:13.461000Z",
  "file_hash": "2ada0b301161f795b5b93062ea0e27dae80d65661846553da593899885dd4f27",
  "private": false,
  "record": {
    "abstract": "A quantum compiler is a software program for decomposing (\"compiling\") an\narbitrary unitary matrix into a sequence of elementary operations (SEO).\nCoppersmith showed that the $\\nb$-bit Discrete Fourier Transform matrix\n$U_{FT}$ can be decomposed in a very efficient way, as a sequence of\norder($\\nb^2$) elementary operations. Can a quantum compiler that doesn\u0027t know\na priori about Coppersmith\u0027s decomposition nevertheless decompose $U_{FT}$ as a\nsequence of order($\\nb^2$) elementary operations? In other words, can it\nrediscover Coppersmith\u0027s decomposition by following a much more general\nalgorithm? Yes it can, if that more general algorithm is the recursive\napplication of the Cosine-Sine Decomposition (CSD).",
    "arxiv_id": "quant-ph/0411097",
    "authors": [
      "Robert R. Tucci"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Fast Fourier Transform Viewed as a Special Case of Recursive   Application of Cosine-Sine Decomposition",
    "url": "https://arxiv.org/abs/quant-ph/0411097"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "07f7d5d2-ec21-4d77-afbf-8ff178e97451",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}