Learning Low-Energy Subspace Overlaps in Many-Body Systems with Measurement-Based and Coherent Quantum Strategies

Quantum Physics arXiv:2607.00235 (quant-ph) [Submitted on 30 Jun 2026] Title:Learning Low-Energy Subspace Overlaps in Many-Body Systems with Measurement-Based and Coherent Quantum Strategies Authors:Shamminuj Aktar, Rishabh Bhardwaj, Tanmoy Bhattacharya, Stephan Eidenbenz View a PDF of the paper titled Learning Low-Energy Subspace Overlaps in Many-Body Systems with Measurement-Based and Coherent Quantum Strategies, by Shamminuj Aktar and 3 other authors View PDF HTML (experimental) Abstract:Predicting the overlap of quantum states with specified low-energy subspaces is a key diagnostic for quantum many-body dynamics, with direct applications in state preparation, subspace-based algorithms, and the study of thermalization. We study the supervised prediction of subspace overlaps O_K between time-evolved states and K-dimensional low-energy eigenspaces of a 10-qubit Heisenberg spin chain following a local perturbation. We compare two quantum information extraction strategies: measurement-based learning, in which classical shadow features are processed by convolutional neural networks, and coherent quantum learning, in which quantum convolutional neural networks process the state directly. We further introduce physics-informed variants for both approaches, including Hamiltonian-aware shadows and QCNN gates aligned with the Heisenberg exchange structure. Across five dataset configurations spanning weak, moderate, and strong quench regimes, physics-informed QCNNs achieve stable performance, with mean test-set coefficients of determination R^2 = 0.753-0.846. Shadow-based methods show stronger regime dependence: they outperform QCNNs in the moderate-quench regime, reaching R^2 = 0.886, but underperform in weak and strong quenches at default shot budgets, where the best shadow results are R^2 = 0.615 and 0.672, respectively. Hardware validation on Quantinuum and IBM noise models shows that arbitrary state preparation is the dominant limitation, requiring approximately 2,044 two-qubit gates and causing near-complete depolarization before inference. These results identify a regime-dependent tradeoff between measurement-based and coherent quantum learning, with shadow methods excelling when the target remains locally accessible and physics-informed QCNNs providing more robust performance across dynamical regimes. Subjects: Quantum Physics (quant-ph) Report number: LA-UR-26-25363 Cite as: arXiv:2607.00235 [quant-ph] (or arXiv:2607.00235v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.00235 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shamminuj Aktar [view email] [v1] Tue, 30 Jun 2026 22:25:38 UTC (253 KB) Full-text links: Access Paper: View a PDF of the paper titled Learning Low-Energy Subspace Overlaps in Many-Body Systems with Measurement-Based and Coherent Quantum Strategies, by Shamminuj Aktar and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)