{
  "annotation_id": "ee83f5c8-7e1e-435f-b908-434035c1a00e",
  "date_created": "2026-03-02T18:02:19.341000Z",
  "date_modified": "2026-03-02T18:02:19.341000Z",
  "file_hash": "f3a011ff431e888aaacc3feb4a68706577d1cceddaf9ae81d258f2b4e2ba0775",
  "private": false,
  "record": {
    "abstract": "This paper presents no new results; its goals are purely pedagogical. A\nspecial case of the Cartan Decomposition has found much utility in the field of\nquantum computing, especially in its sub-field of quantum compiling. This\nspecial case allows one to factor a general 2-qubit operation (i.e., an element\nof U(4)) into local operations applied before and after a three parameter,\nnon-local operation. In this paper, we give a complete and rigorous proof of\nthis special case of Cartan\u0027s Decomposition. From the point of view of QC\nprogrammers who might not be familiar with the subtleties of Lie Group Theory,\nthe proof given here has the virtues, that it is constructive in nature, and\nthat it uses only Linear Algebra. The constructive proof presented in this\npaper is implemented in some Octave/Matlab m-files that are included with the\npaper. Thus, this paper serves as documentation for the attached m-files.",
    "arxiv_id": "quant-ph/0507171",
    "authors": [
      "Robert R. Tucci"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An Introduction to Cartan\u0027s KAK Decomposition for QC Programmers",
    "url": "https://arxiv.org/abs/quant-ph/0507171"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "902fe5d3-a3dd-46f0-99ad-39176c41ae25",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}