{"paper":{"title":"Quantum algorithm for estimating volumes of convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"quant-ph","authors_text":"Andrew M. Childs, Chunhao Wang, Shih-Han Hung, Shouvanik Chakrabarti, Tongyang Li, Xiaodi Wu","submitted_at":"2019-08-11T13:13:47Z","abstract_excerpt":"Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an $n$-dimensional convex body within multiplicative error $\\epsilon$ using $\\tilde{O}(n^{3}+n^{2.5}/\\epsilon)$ queries to a membership oracle and $\\tilde{O}(n^{5}+n^{4.5}/\\epsilon)$ additional arithmetic operations. For comparison, the best known classical algorithm uses $\\tilde{O}(n^{4}+n^{3}/\\epsilon^{2})$ queries and $\\tilde{O}(n^{6}+n^{5}/\\epsilon^{2})$ additional arithmetic operations. To the best"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03903","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03903/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}