{"paper":{"title":"A Quantum Interior Point Method for LPs and SDPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, Iordanis Kerenidis","submitted_at":"2018-08-28T13:10:03Z","abstract_excerpt":"We present a quantum interior point method with worst case running time $\\widetilde{O}(\\frac{n^{2.5}}{\\xi^{2}} \\mu \\kappa^3 \\log (1/\\epsilon))$ for SDPs and $\\widetilde{O}(\\frac{n^{1.5}}{\\xi^{2}} \\mu \\kappa^3 \\log (1/\\epsilon))$ for LPs, where the output of our algorithm is a pair of matrices $(S,Y)$ that are $\\epsilon$-optimal $\\xi$-approximate SDP solutions. The factor $\\mu$ is at most $\\sqrt{2}n$ for SDPs and $\\sqrt{2n}$ for LP's, and $\\kappa$ is an upper bound on the condition number of the intermediate solution matrices. For the case where the intermediate matrices for the interior point "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09266","kind":"arxiv","version":1},"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"}