quantum-computing

Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization

arXiv Quantum Physics

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⚡ Quantum Brief

Researchers led by Jie Wang introduced a scalable method to certify ground-state properties in quantum spin systems using structured noncommutative polynomial optimization, addressing a longstanding challenge in many-body quantum physics. The team reformulates ground-state calculations as optimization problems solvable via semidefinite programming, unlike traditional variational methods, enabling both lower energy bounds and observable expectation value ranges. A key breakthrough is leveraging inherent system symmetries to overcome scalability barriers, extending applicability from small systems to 16×16 square lattices—unprecedented for this approach. Semidefinite relaxations provide rigorous bounds on ground-state energies and observables, offering advantages over ansatz-dependent variational techniques that lack guaranteed convergence or lower-bound certification. Published in April 2026, the work bridges quantum physics and optimization theory, with potential impacts on quantum simulation, material science, and error-mitigated quantum computing.

Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization

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Quantum Physics arXiv:2604.01555 (quant-ph) [Submitted on 2 Apr 2026] Title:Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization Authors:Jie Wang, David Jansen, Irénée Frerot, Marc-Olivier Renou, Victor Magron, Antonio Acín View a PDF of the paper titled Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization, by Jie Wang and 5 other authors View PDF HTML (experimental) Abstract:A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over the possible states expressible by this ansatz, one can alternatively formulate the problem as a noncommutative polynomial optimization problem. This optimization problem can then be addressed using a hierarchy of semidefinite programming relaxations. In contrast to variational calculations, the semidefinite program can provide lower bounds for ground state energies and upper and lower bounds on observable expectation values. However, this approach typically suffers from severe scalability issues, limiting its applicability to small-to-medium-scale systems. In this article, we demonstrate that leveraging the inherent structures of the system can significantly mitigate these scalability challenges and thus allows us to compute meaningful bounds for quantum spin systems on up to $16\times16$ square lattices. Comments: Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) MSC classes: 90C23, 81-08, 47N10 Cite as: arXiv:2604.01555 [quant-ph] (or arXiv:2604.01555v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.01555 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jie Wang [view email] [v1] Thu, 2 Apr 2026 03:00:01 UTC (59 KB) Full-text links: Access Paper: View a PDF of the paper titled Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization, by Jie Wang and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: math math.OC 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?)

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Source: arXiv Quantum Physics

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