{
  "annotation_id": "896522df-008d-4b1e-9131-7fcb7566af2c",
  "date_created": "2026-03-02T18:02:37.232000Z",
  "date_modified": "2026-03-02T18:02:37.232000Z",
  "file_hash": "aca75bfee0e3aad7fa0803369544203c66c560e30c450dfff731b9f9607712e2",
  "private": false,
  "record": {
    "abstract": "We study quantum systems with even numbers N of levels that are completely\nstate-controlled by unitary transformations generated by Lie algebras\nisomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than\nthe respective su(N) with dimension N^2-1. We show that this reduction\nconstrains the Hamiltonian to have symmetric energy levels. An example of such\na system is an n-qubit system. Using a geometric representation for the quantum\nwave function of a finite system, we present an explicit example that shows a\ntwo-qubit system can be controlled by the elements of the Lie algebra sp(4)\n(isomorphic to spin(5) and so(5)) with dimension ten rather than su(4) with\ndimension fifteen. These results enable one to envision more efficient\nalgorithms for the design of fields for quantum-state engineering, and they\nprovide more insight into the fundamental structure of quantum control.",
    "arxiv_id": "quant-ph/0703220",
    "authors": [
      "R. Cabrera",
      "C. Rangan",
      "W. E. Baylis"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.76.033401",
    "title": "Overcoming the su(2^n) sufficient condition for the coherent control of   n-qubit systems",
    "url": "https://arxiv.org/abs/quant-ph/0703220"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4fa6adc4-ef2a-4eac-bf40-521876fa7f60",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}