{"paper":{"title":"Revisiting Quantum Algorithms for Linear Regressions: Quadratic Speedups without Data-Dependent Parameters","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"quant-ph","authors_text":"Junze Yin, Ruizhe Zhang, Zhao Song","submitted_at":"2023-11-24T19:41:28Z","abstract_excerpt":"Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \\in \\mathbb{R}^{n \\times d}$ and a vector $b$, the goal is to find $x'$ such that\n  $ \\| Ax' - b \\|_2^2 \\leq (1+\\epsilon) \\min_{x} \\| A x - b \\|_2^2 $. The best classical algorithm takes $O(nd) + \\mathrm{poly}(d/\\epsilon)$ time [Clarkson and Woodruff STOC 2013, Nelson and Nguyen FOCS 2013]. On the other hand, quantum linear regression algorithms can achieve exponential quantum speedups, as shown in [Wang Phys. Rev. A 96, 012335, Kerenidis and Prakash ITCS 2017, Chakraborty, Gily{\\'e}n and Jeffery "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.14823","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/2311.14823/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"}