{
  "id": "quant-ph/0603009",
  "version": "v3",
  "published": "2006-03-01T16:17:41.000Z",
  "updated": "2006-09-08T13:59:58.000Z",
  "title": "Deciding universality of quantum gates",
  "authors": [
    "Gabor Ivanyos"
  ],
  "comment": "8 pages, minor corrections",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We say that collection of $n$-qudit gates is universal if there exists $N_0\\geq n$ such that for every $N\\geq N_0$ every $N$-qudit unitary operation can be approximated with arbitrary precision by a circuit built from gates of the collection. Our main result is an upper bound on the smallest $N_0$ with the above property. The bound is roughly $d^8 n$, where $d$ is the number of levels of the base system (the '$d$' in the term qu$d$it.) The proof is based on a recent result on invariants of (finite) linear groups.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-09-08T13:59:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum gates",
      "deciding universality",
      "qudit unitary operation",
      "qudit gates",
      "collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006quant.ph..3009I"
    }
  }
}