Local-Observable-Guided Generative Quantum Circuits for Degenerate Ground Spaces
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Quantum Physics arXiv:2605.23300 (quant-ph) [Submitted on 22 May 2026] Title:Local-Observable-Guided Generative Quantum Circuits for Degenerate Ground Spaces Authors:Yiying Chen, Lingxia Zhang, Yanzheng Zhu, Kaiyan Yang, Xiao Zeng, Zizhu Wang View a PDF of the paper titled Local-Observable-Guided Generative Quantum Circuits for Degenerate Ground Spaces, by Yiying Chen and 4 other authors View PDF HTML (experimental) Abstract:Searching for degenerate ground spaces in quantum many-body systems is central to understanding spontaneous symmetry breaking and topological order. Although existing numerical methods can approximate individual ground states with high accuracy, recovering the full degenerate space remains a substantial challenge. Here we tackle this problem using a hybrid generative quantum circuit that combines a classical generative model with an expressive parameterized quantum circuit (PQC). The classical model learns a distribution over PQC parameters, enabling the sampling of an ensemble of ground states, while the PQC ensures compatibility with quantum hardware. To promote both low energy and state diversity, we define an energy-diversity objective composed of an energy-minimization term and cosine-similarity penalties derived from local observable correlators. These local descriptors provide a scalable, measurement-efficient means of distinguishing distinct ground states. We benchmark the framework on the Majumdar-Ghosh model, the Affleck-Kennedy-Lieb-Tasaki model, and the spin-1 XXZ chain, which realize distinct mechanisms of degeneracy. In all cases, the method produces a diverse ensemble whose linear span accurately reproduces the target ground space, in some instances, it identifies an approximately orthogonal basis within the learned ensemble. We further show that the framework remains robust under shot-based estimation and can still recover the degenerate ground space with a reduced measurement budget. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.23300 [quant-ph] (or arXiv:2605.23300v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.23300 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zizhu Wang [view email] [v1] Fri, 22 May 2026 07:17:50 UTC (7,818 KB) Full-text links: Access Paper: View a PDF of the paper titled Local-Observable-Guided Generative Quantum Circuits for Degenerate Ground Spaces, by Yiying Chen and 4 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?)