Comparing Classical Simulation and Sample-Based Learning of Quantum Systems: Learning the Hardness of Quantum Systems from Samples
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Quantum Physics arXiv:2605.28986 (quant-ph) [Submitted on 27 May 2026] Title:Comparing Classical Simulation and Sample-Based Learning of Quantum Systems: Learning the Hardness of Quantum Systems from Samples Authors:João Pedro Del Rey, Raúl O. Vallejos, Fernando de Melo View a PDF of the paper titled Comparing Classical Simulation and Sample-Based Learning of Quantum Systems: Learning the Hardness of Quantum Systems from Samples, by Jo\~ao Pedro Del Rey and 2 other authors View PDF HTML (experimental) Abstract:We investigate the relationship between two distinct classical approaches to quantum systems: direct simulation from a classical description and sample-based learning from measurement data. While both tasks ultimately aim to reproduce Born-rule statistics, complexity-theoretic results suggest that simulability and learnability need not coincide in general. Here we study this relationship empirically using a fixed deep energy-based generative model trained on measurement samples from controlled families of quantum states. We independently tune two quantum resources associated with classical simulation cost: entanglement, through the bond dimension of random matrix product states, and non-stabilizerness, through the number of T gates in Clifford-dominated circuits. Learning difficulty is characterized using two probes of neural-network complexity: the largest Hessian eigenvalue at convergence and Random Subspace Optimization. For both quantum resources, increasing simulation hardness systematically correlates with sharper loss landscapes and degraded reconstruction performance under constrained capacity. Our results indicate that, within the regimes studied here, classical learnability tracks known simulation complexity measures, suggesting that neural-network training dynamics can provide an empirical probe of quantum computational hardness. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.28986 [quant-ph] (or arXiv:2605.28986v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.28986 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: João Pedro Del Rey [view email] [v1] Wed, 27 May 2026 18:44:36 UTC (1,498 KB) Full-text links: Access Paper: View a PDF of the paper titled Comparing Classical Simulation and Sample-Based Learning of Quantum Systems: Learning the Hardness of Quantum Systems from Samples, by Jo\~ao Pedro Del Rey and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)