{
  "annotation_id": "68fe3504-a1bc-420a-9b1f-46eba87529b0",
  "date_created": "2026-03-02T18:02:23.418000Z",
  "date_modified": "2026-03-02T18:02:23.418000Z",
  "file_hash": "6e74d09e605a43e932fc529f4c45bdb58dcbd738df83bb45ea79ce3cfd0385cb",
  "private": false,
  "record": {
    "abstract": "We consider quantum computational models defined via a Lie-algebraic theory.\nIn these models, specified initial states are acted on by Lie-algebraic quantum\ngates and the expectation values of Lie algebra elements are measured at the\nend. We show that these models can be efficiently simulated on a classical\ncomputer in time polynomial in the dimension of the algebra, regardless of the\ndimension of the Hilbert space where the algebra acts. Similar results hold for\nthe computation of the expectation value of operators implemented by a\ngate-sequence. We introduce a Lie-algebraic notion of generalized mean-field\nHamiltonians and show that they are efficiently (\"exactly\") solvable by means\nof a Jacobi-like diagonalization method. Our results generalize earlier ones on\nfermionic linear optics computation and provide insight into the source of the\npower of the conventional model of quantum computation.",
    "arxiv_id": "quant-ph/0601030",
    "authors": [
      "Rolando Somma",
      "Howard Barnum",
      "Gerardo Ortiz",
      "Emanuel Knill"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.other"
    ],
    "doi": "10.1103/PhysRevLett.97.190501",
    "title": "Efficient solvability of Hamiltonians and limits on the power of some   quantum computational models",
    "url": "https://arxiv.org/abs/quant-ph/0601030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8f27c183-8718-479f-836f-d91e34404f6e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}