{"paper":{"title":"A quantum linear system algorithm for dense matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, Leonard Wossnig, Zhikuan Zhao","submitted_at":"2017-04-20T14:47:34Z","abstract_excerpt":"Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation. Given a matrix $A$ and a vector $\\mathbf b$ the task is to find the vector $\\mathbf x$ such that $A \\mathbf x = \\mathbf b$. We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of $\\mathcal{O}(\\kappa^2 \\|A\\|_F \\text{polylog}(n)/\\epsilon)$, where $n\\times n$ is the dimensionality of $A$ with Frobenius norm $\\|A\\|_F$, $\\kappa$ denotes the condition number of $A$, and $\\epsilon$ is the desired precision parameter. When applied to a dense matrix with spectra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06174","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"}