O-Sensing: Operator Sensing for Interaction Geometry and Symmetries
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Quantum Physics arXiv:2603.03826 (quant-ph) [Submitted on 4 Mar 2026] Title:O-Sensing: Operator Sensing for Interaction Geometry and Symmetries Authors:Meng Ye-Ming, Shi Zhe-Yu View a PDF of the paper titled O-Sensing: Operator Sensing for Interaction Geometry and Symmetries, by Meng Ye-Ming and Shi Zhe-Yu View PDF HTML (experimental) Abstract:We ask whether the Hamiltonian, interaction geometry, and symmetries of a quantum many-body system can be inferred from a few low-lying eigenstates without knowing which sites interact with each other. Directly solving the eigenvalue equations imposes constraints that yield a highly degenerate subspace of candidate operators, where the local Hamiltonian is hidden among an extensive family of conserved quantities, obscuring the interaction geometry. Here we introduce O-Sensing, a protocol designed to extract the Hamiltonian and symmetries directly from these states. Specifically, O-Sensing employs parsimony-driven optimization to extract a maximally sparse operator basis from the degenerate subspace. The Hamiltonian is then selected from this basis by maximizing spectral entropy (effectively minimizing degeneracy) within the sampled subspace. We validate O-Sensing on Heisenberg models on connected Erdős--Rényi graphs, where it reconstructs the interaction geometry and uncovers additional long-range conserved operators. We establish a learnability phase diagram across graph densities, featuring a pronounced ``confusion'' regime where parsimony favors a dual description on the complement graph. These results show that sparsity optimization can reconstruct interaction geometry as an emergent output, enabling simultaneous recovery of the Hamiltonian and its symmetries from low-energy eigenstates. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Data Analysis, Statistics and Probability (physics.data-an) Cite as: arXiv:2603.03826 [quant-ph] (or arXiv:2603.03826v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.03826 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ye-Ming Meng [view email] [v1] Wed, 4 Mar 2026 08:24:43 UTC (972 KB) Full-text links: Access Paper: View a PDF of the paper titled O-Sensing: Operator Sensing for Interaction Geometry and Symmetries, by Meng Ye-Ming and Shi Zhe-YuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el physics physics.data-an 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?)