{"paper":{"title":"Quantum algorithm for systems of linear equations with exponentially improved dependence on precision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andrew M. Childs, Robin Kothari, Rolando D. Somma","submitted_at":"2015-11-07T05:42:01Z","abstract_excerpt":"Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \\times N$ matrix $A$ and $N$-dimensional vector $\\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of equations $A\\vec{x}=\\vec{b}$. If $A$ is sparse and well-conditioned, their algorithm runs in time $\\mathrm{poly}(\\log N, 1/\\epsilon)$, where $\\epsilon$ is the desired precision in the output state. We improve this to an algorithm whose running time is polynomial in $\\log(1/\\epsilon)$, exponentially improving the dependence on precision while keeping essentiall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02306","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"}