{"paper":{"title":"Quantum algorithms for Second-Order Cone Programming and Support Vector Machines","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, D\\'aniel Szil\\'agyi, Iordanis Kerenidis","submitted_at":"2019-08-19T12:02:13Z","abstract_excerpt":"We present a quantum interior-point method (IPM) for second-order cone programming (SOCP) that runs in time $\\widetilde{O} \\left( n\\sqrt{r} \\frac{\\zeta \\kappa}{\\delta^2} \\log \\left(1/\\epsilon\\right) \\right)$ where $r$ is the rank and $n$ the dimension of the SOCP, $\\delta$ bounds the distance of intermediate solutions from the cone boundary, $\\zeta$ is a parameter upper bounded by $\\sqrt{n}$, and $\\kappa$ is an upper bound on the condition number of matrices arising in the classical IPM for SOCP. The algorithm takes as its input a suitable quantum description of an arbitrary SOCP and outputs a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06720","kind":"arxiv","version":4},"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/1908.06720/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"}