Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
Summarize this article with:
Quantum Physics arXiv:2606.07825 (quant-ph) [Submitted on 5 Jun 2026] Title:Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States Authors:Hang Zhang, Victor Armegioiu, Juan Carrasquilla, Siddhartha Mishra, Johannes Müller, Jannes Nys, Marius Zeinhofer View a PDF of the paper titled Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States, by Hang Zhang and 6 other authors View PDF HTML (experimental) Abstract:Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems fraught with competing orders and nearly degenerate ground states, such as frustrated magnets and strongly correlated electron materials. Here, we introduce Projected Inverse Iteration (PII) by re-framing the ground-state search as an eigenvalue problem. PII achieves rapid, gap-insensitive convergence while preserving the favorable polynomial computational scaling of stochastic reconfiguration. Demonstrated on challenging two-dimensional spin systems, including the highly frustrated $J_1$-$J_2$ model, PII outperforms standard optimization techniques and presents a promising algorithmic strategy for discovering complex quantum states in the presence of small spectral gaps. More broadly, PII can be interpreted as a novel natural gradient method tailored for eigenvalue problems, opening up its application to related challenges within deep learning. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.07825 [quant-ph] (or arXiv:2606.07825v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.07825 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Marius Zeinhofer [view email] [v1] Fri, 5 Jun 2026 20:23:38 UTC (2,192 KB) Full-text links: Access Paper: View a PDF of the paper titled Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States, by Hang Zhang and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)