{
  "annotation_id": "5a72045e-4dd8-4d75-9b98-694011dfb77b",
  "date_created": "2026-03-02T18:01:49.498000Z",
  "date_modified": "2026-03-02T18:01:49.498000Z",
  "file_hash": "bd1ef6c48e3ebfbb96254d942bf346ab7915e38fa4a1f8206ed52d1b589acdd0",
  "private": false,
  "record": {
    "abstract": "Consider a compact connected Lie group $G$ and the corresponding Lie algebra\n$\\cal L$. Let $\\{X_1,...,X_m\\}$ be a set of generators for the Lie algebra\n$\\cal L$. We prove that $G$ is uniformly finitely generated by\n$\\{X_1,...,X_m\\}$. This means that every element $K \\in G$ can be expressed as\n$K=e^{Xt_1}e^{Xt_2} \\cdot \\cdot \\cdot e^{Xt_l}$, where the indeterminates $X$\nare in the set $\\{X_1,...,X_m \\}$, $t_i \\in \\RR$, $i=1,...,l$, and the number\n$l$ is uniformly bounded. This extends a previous result by F. Lowenthal in\nthat we do not require the connected one dimensional Lie subgroups\ncorresponding to the $X_i$, $i=1,...,m$, to be compact.\n  We discuss the consequence of this result to the question of universality of\nquantum gates in quantum computing.",
    "arxiv_id": "quant-ph/0111133",
    "authors": [
      "D. D\u0027Alessandro"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Uniform Finite Generation of Compact Lie Groups and universal quantum   gates",
    "url": "https://arxiv.org/abs/quant-ph/0111133"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "53a2f212-c41a-4a16-834f-66a0b5a80d3b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}