{
  "annotation_id": "94ae2c0e-b88b-4c09-8cb7-9300a37f1e72",
  "date_created": "2026-03-02T18:02:02.266000Z",
  "date_modified": "2026-03-02T18:02:02.266000Z",
  "file_hash": "f851cc8595d6d0f7d5c771d16e046f7e2205996092ee2ad812f544c54fa8735e",
  "private": false,
  "record": {
    "abstract": "The dynamics of a quantum system driven by an external field is well\ndescribed by a unitary transformation generated by a time dependent\nHamiltonian. The inverse problem of finding the field that generates a specific\nunitary transformation is the subject of study. The unitary transformation\nwhich can represent an algorithm in a quantum computation is imposed on a\nsubset of quantum states embedded in a larger Hilbert space. Optimal control\ntheory (OCT) is used to solve the inversion problem irrespective of the initial\ninput state. A unified formalism, based on the Krotov method is developed\nleading to a new scheme. The schemes are compared for the inversion of a\ntwo-qubit Fourier transform using as registers the vibrational levels of the\n$X^1\\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the\n$A^1\\Sigma^+_u$ electronic state induce the transitions. Light fields are found\nthat are able to implement the Fourier transform within a picosecond time\nscale. Such fields can be obtained by pulse-shaping techniques of a femtosecond\npulse. Out of the schemes studied the square modulus scheme converges fastest.\nA study of the implementation of the $Q$ qubit Fourier transform in the Na$_2$\nmolecule was carried out for up to 5 qubits. The classical computation effort\nrequired to obtain the algorithm with a given fidelity is estimated to scale\nexponentially with the number of levels. The observed moderate scaling of the\npulse intensity with the number of qubits in the transformation is\nrationalized.",
    "arxiv_id": "quant-ph/0309011",
    "authors": [
      "Jose P. Palao",
      "R. Kosloff"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.68.062308",
    "title": "Optimal control theory for unitary transformations",
    "url": "https://arxiv.org/abs/quant-ph/0309011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ddead92c-c94b-4aff-9cdf-22a65443a681",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}