{"paper":{"title":"Faster quantum linear system solver beyond the condition number","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DS","cs.NA","math.NA"],"primary_cat":"quant-ph","authors_text":"Alexander M. Dalzell, Jianqiang Li, Yuan Su","submitted_at":"2026-07-08T17:49:40Z","abstract_excerpt":"The spectral condition number is a widely adopted measure of worst-case cost for quantum linear system solvers. Yet it can significantly overestimate the actual runtime for a typical problem instance. We present two quantum algorithms that produce the normalized solution $|x\\rangle$ of linear system $Ax=| b \\rangle$ to accuracy $\\epsilon$ with complexity independent of the condition number $\\kappa=\\lVert A^{-1}\\rVert$. We focus on the standard input model where $A$ is accessed through a block encoding and $| b \\rangle$ is prepared by a unitary. But we also introduce an affine dilation model th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07691","kind":"arxiv","version":1},"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/2607.07691/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"}