{"paper":{"title":"Faster quantum-inspired algorithms for solving linear systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"quant-ph","authors_text":"Ashley Montanaro, Changpeng Shao","submitted_at":"2021-03-18T15:12:44Z","abstract_excerpt":"We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\\x = \\b$, we show that there is a classical algorithm that outputs a data structure for $\\x$ allowing sampling and querying to the entries, where $\\x$ is such that $\\|\\x - A^{+}\\b\\|\\leq \\epsilon \\|A^{+}\\b\\|$. This output can be viewed as a classical analogue to the output of quantum linear solvers. The complexity of our algorithm is $\\widetilde{O}(\\kappa_F^4 \\kappa^2/\\epsilon^2 )$, where $\\kappa_F = \\|A\\|_F\\|A^{+}\\|$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.10309","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.10309/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"}