Constant Factor Analysis of Optimal Quantum Linear Solvers in Practice
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Quantum Physics arXiv:2604.22185 (quant-ph) [Submitted on 24 Apr 2026] Title:Constant Factor Analysis of Optimal Quantum Linear Solvers in Practice Authors:Pedro C. S. Costa, Alexander M. Dalzell, Dong An, Dominic W. Berry View a PDF of the paper titled Constant Factor Analysis of Optimal Quantum Linear Solvers in Practice, by Pedro C. S. Costa and 3 other authors View PDF HTML (experimental) Abstract:Optimal quantum linear equation solvers provide complexity $O(\kappa\log(1/\epsilon))$, where $\kappa$ is the condition number and $\epsilon$ is the allowable error. The optimal solver using a discrete adiabatic approach [PRX Quantum \textbf{3}, 040303 (2022)] has large analytically proven constant factors for the upper bound on the complexity. The constant factors were later found to be about 1,200 times smaller in numerical testing [Quantum \textbf{9}, 1887 (2025)]. This meant it is about an order of magnitude more efficient than using a randomised approach from [PRX Quantum \textbf{6}, 040373 (2025)], which has far smaller analytically proven constant factors. Recently, a ``Shortcut'' method has been found to provide an optimal solver which also has small proven constant factors. In the present work, we conduct a comprehensive numerical analysis comparing this method with the adiabatic solver for two families of random linear systems. We find that, in the case where the solution norm is \emph{unknown}, the adiabatic solver provides slightly better performance. If the solution norm is \emph{known}, then the shortcut method provides significantly better performance for non-Hermitian matrices. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.22185 [quant-ph] (or arXiv:2604.22185v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.22185 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pedro C.S. Costa [view email] [v1] Fri, 24 Apr 2026 03:23:09 UTC (1,199 KB) Full-text links: Access Paper: View a PDF of the paper titled Constant Factor Analysis of Optimal Quantum Linear Solvers in Practice, by Pedro C. S. Costa and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)