{
  "annotation_id": "3846606a-81a7-4d54-b7fc-596f69fc8872",
  "date_created": "2026-03-02T18:02:23.666000Z",
  "date_modified": "2026-03-02T18:02:23.666000Z",
  "file_hash": "73c22779f6b1ab380773c7326125e4bbcc962ff3eb3f9bee8a75c9269662e837",
  "private": false,
  "record": {
    "abstract": "We say that collection of $n$-qudit gates is universal if there exists\n$N_0\\geq n$ such that for every $N\\geq N_0$ every $N$-qudit unitary operation\ncan be approximated with arbitrary precision by a circuit built from gates of\nthe collection. Our main result is an upper bound on the smallest $N_0$ with\nthe above property. The bound is roughly $d^8 n$, where $d$ is the number of\nlevels of the base system (the \u0027$d$\u0027 in the term qu$d$it.) The proof is based\non a recent result on invariants of (finite) linear groups.",
    "arxiv_id": "quant-ph/0603009",
    "authors": [
      "Gabor Ivanyos"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Deciding universality of quantum gates",
    "url": "https://arxiv.org/abs/quant-ph/0603009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e36f59ea-0cc9-4109-9171-7e52a78e25e2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}