{
  "annotation_id": "5e42ca86-d9df-474d-bca7-a21cf230d0cb",
  "date_created": "2026-03-02T18:02:13.026000Z",
  "date_modified": "2026-03-02T18:02:13.026000Z",
  "file_hash": "925ee31bef5024e50b885d4cc4ffcad7a563a2b4a0334311db1f44b27dcd0c9f",
  "private": false,
  "record": {
    "abstract": "Four-level systems in quantum optics, and for representing two qubits in\nquantum computing, are difficult to solve for general time-dependent\nHamiltonians. A systematic procedure is presented which combines analytical\nhandling of the algebraic operator aspects with simple solutions of classical,\nfirst-order differential equations. In particular, by exploiting $su(2) \\oplus\nsu(2)$ and $su(2) \\oplus su(2) \\oplus u(1)$ sub-algebras of the full SU(4)\ndynamical group of the system, the non-trivial part of the final calculation is\nreduced to a single Riccati (first order, quadratically nonlinear) equation,\nitself simply solved. Examples are provided of two-qubit problems from the\nrecent literature, including implementation of two-qubit gates with Josephson\njunctions.",
    "arxiv_id": "quant-ph/0501048",
    "authors": [
      "A. R. P. Rau",
      "G. Selvaraj",
      "D. Uskov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.062316",
    "journal_ref": "Phys.Rev.A71:062316,2005",
    "title": "Four-level and two-qubit systems, sub-algebras, and unitary integration",
    "url": "https://arxiv.org/abs/quant-ph/0501048"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "530e28e7-b4de-4a69-a604-44e420a39ca9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}