When Does Quantum Annealing Outperform Classical Methods? A Gradient Variance Framework
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Quantum Physics arXiv:2602.16875 (quant-ph) [Submitted on 18 Feb 2026] Title:When Does Quantum Annealing Outperform Classical Methods? A Gradient Variance Framework Authors:Vishwajeet Ohal, Pierre Boulanger View a PDF of the paper titled When Does Quantum Annealing Outperform Classical Methods? A Gradient Variance Framework, by Vishwajeet Ohal and Pierre Boulanger View PDF HTML (experimental) Abstract:Based on our experimental findings, we propose the following decision framework for practitioners. Quantum annealing is recommended when the problem formulation QUBO exhibits a high gradient variance (greater than 0.3) and the energy landscape contains numerous thin barriers characterized by sharp peaks and narrow valleys. Additionally, quantum approaches are particularly suitable when classical methods are observed to get trapped in local minima, the problem size is manageable given hardware constraints (less than 5000 variables for pure quantum annealing), and the time overhead of approximately 10 seconds is acceptable for the application. In contrast, classical methods are recommended when the gradient variance is low (less than 0.2), indicating smooth landscapes where quantum tunneling provides little advantage. Classical approaches are also preferable when the problem size is small and classical solvers can provide nearly instantaneous results, when solution quality requirements are modest and local optima suffice, or when hardware access or cost is a limiting factor. For problems that exceed pure quantum capacity but possess a favorable landscape structure, hybrid approaches combining quantum and classical techniques are recommended. Such hybrid methods are particularly effective when decomposition quality can be verified and both solution quality and scalability are important considerations. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.16875 [quant-ph] (or arXiv:2602.16875v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.16875 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Vishwajeet Ohal [view email] [v1] Wed, 18 Feb 2026 21:00:48 UTC (721 KB) Full-text links: Access Paper: View a PDF of the paper titled When Does Quantum Annealing Outperform Classical Methods? A Gradient Variance Framework, by Vishwajeet Ohal and Pierre BoulangerView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)