{"paper":{"title":"Universality of single qudit gates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GR","math.MP"],"primary_cat":"quant-ph","authors_text":"Adam Sawicki, Katarzyna Karnas","submitted_at":"2016-09-19T15:29:06Z","abstract_excerpt":"We consider the problem of deciding if a set of quantum one-qudit gates $\\mathcal{S}=\\{g_1,\\ldots,g_n\\}\\subset G$ is universal, i.e if the closure $\\overline{<\\mathcal{S}>}$ is equal to $G$, where $G$ is either the special unitary or the special orthogonal group. To every gate $g$ in $\\mathcal{S}$ we asign its image under the adjoint representation $\\mathrm{Ad}_g$, where $\\mathrm{Ad}:G\\rightarrow SO(\\mathfrak{g})$ and $\\mathfrak{g}$ is the Lie algebra of $G$. The necessary condition for the universality of $\\mathcal{S}$ is that the only matrices that commute with all $\\mathrm{Ad}_{g_i}$'s are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05780","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}