{"paper":{"title":"Quantum Speed-ups for Semidefinite Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Fernando G.S.L. Brandao, Krysta Svore","submitted_at":"2016-09-18T20:13:50Z","abstract_excerpt":"We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst-case running time $n^{\\frac{1}{2}} m^{\\frac{1}{2}} s^2 \\text{poly}(\\log(n), \\log(m), R, r, 1/\\delta)$, with $n$ and $s$ the dimension and row-sparsity of the input matrices, respectively, $m$ the number of constraints, $\\delta$ the accuracy of the solution, and $R, r$ a upper bounds on the size of the optimal primal and dual solutions. This gives a square-root unconditional speed-up over any classical method for solving SDPs both in $n$ and $m$. We prove the algorithm cannot be substantially improved (in terms o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05537","kind":"arxiv","version":5},"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"}