{"paper":{"title":"Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lin Chen, Li Yu","submitted_at":"2015-01-12T16:41:46Z","abstract_excerpt":"We show that any unitary operator on the $d_A\\times d_B$ system ($d_A\\ge 2$) can be decomposed into the product of at most $4d_A-5$ controlled unitary operators. The number can be reduced to $2d_A-1$ when $d_A$ is a power of two. We also prove that three controlled unitaries can implement a bipartite complex permutation operator, and discuss the connection to an analogous result on classical reversible circuits. We further show that any $n$-partite unitary on the space $\\mathbb{C}^{d_1}\\otimes...\\otimes\\mathbb{C}^{d_n}$ is the product of at most $[2\\prod^{n-1}_{j=1}(2d_j-2)-1]$ controlled unit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02708","kind":"arxiv","version":2},"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"}