{
  "annotation_id": "8fe79b89-9f0b-4fbd-856b-ab173f8d78c6",
  "date_created": "2026-03-02T18:02:06.650000Z",
  "date_modified": "2026-03-02T18:02:06.650000Z",
  "file_hash": "041aacbb25ece1372d7df4f116ad580b93d8c178d897ebd688573c2bce8b5afe",
  "private": false,
  "record": {
    "abstract": "The isoholonomic problem in a homogeneous bundle is formulated and solved\nexactly. The problem takes a form of a boundary value problem of a variational\nequation. The solution is applied to the optimal control problem in holonomic\nquantum computer. We provide a prescription to construct an optimal controller\nfor an arbitrary unitary gate and apply it to a $ k $-dimensional unitary gate\nwhich operates on an $ N $-dimensional Hilbert space with $ N \\geq 2k $. Our\nconstruction is applied to several important unitary gates such as the Hadamard\ngate, the CNOT gate, and the two-qubit discrete Fourier transformation gate.\nControllers for these gates are explicitly constructed.",
    "arxiv_id": "quant-ph/0406038",
    "authors": [
      "Shogo Tanimura",
      "Mikio Nakahara",
      "Daisuke Hayashi"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1835545",
    "journal_ref": "Journal of Mathematical Physics 46 (2005) 022101, 1-15",
    "title": "Exact solutions of the isoholonomic problem and the optimal control   problem in holonomic quantum computation",
    "url": "https://arxiv.org/abs/quant-ph/0406038"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8e6ae53d-afe9-47a8-9811-113dd6ae295e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}