{
  "annotation_id": "dcda769a-e3f5-4f27-9ca0-d91d06834ccc",
  "date_created": "2026-03-02T18:01:46.039000Z",
  "date_modified": "2026-03-02T18:01:46.039000Z",
  "file_hash": "ac426415628cdf11a5cf93cdefa09b2019e31d00782d1003666e0e24c4c14ad1",
  "private": false,
  "record": {
    "abstract": "In this paper we study universality for quantum gates acting on qudits.Qudits\nare states in a Hilbert space of dimension d where d is at least two. We\ndetermine which 2-qudit gates V have the properties (i) the collection of all\n1-qudit gates together with V produces all n-qudit gates up to arbitrary\nprecision, or (ii) the collection of all 1-qudit gates together with V produces\nall n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions\non V, and they hold if and only if V is not a primitive gate. Here we say V is\nprimitive if it transforms any decomposable tensor into a decomposable tensor.\nWe discuss some applications and also relations with work of other authors.",
    "arxiv_id": "quant-ph/0108062",
    "authors": [
      "Jean-Luc Brylinski",
      "Ranee Brylinski"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Universal quantum gates",
    "url": "https://arxiv.org/abs/quant-ph/0108062"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d161b78b-05bf-4a08-b3af-9b1cbe28624d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}