{
  "annotation_id": "d42b3be2-1964-49c2-aa7a-47b3ac1e87b2",
  "date_created": "2026-03-02T18:01:39.264000Z",
  "date_modified": "2026-03-02T18:01:39.264000Z",
  "file_hash": "191a3769197d84c8c74b1eadaf1589b4a95939f0e647327d0c20a3cd1245b618",
  "private": false,
  "record": {
    "abstract": "The quantum Fourier transform (QFT) is a powerful tool in quantum computing.\nThe main ingredients of QFT are formed by the Walsh-Hadamard transform H and\nphase shifts P(.), both of which are 2x2 unitary matrices as operators on the\ntwo-dimensional 1-qubit space. In this paper, we show that H and P(.) suffice\nto generate the unitary group U(2) and, consequently, through controlled-U\noperations and their concatenations, the entire unitary group U(2^n) on\nn-qubits can be generated. Since any quantum computing algorithm in an n-qubit\nquantum computer is based on operations by matrices in U(2^n), in this sense we\nhave the universality of the QFT.",
    "arxiv_id": "quant-ph/0007122",
    "authors": [
      "Charles M. Bowden",
      "Goong Chen",
      "Zijian Diao",
      "Andreas Klappenecker"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The Universality of the Quantum Fourier Transform in Forming the Basis   of Quantum Computing Algorithms",
    "url": "https://arxiv.org/abs/quant-ph/0007122"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3415d8aa-384d-485c-a4e4-8403f90a47a8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}