Near-frustration-free electronic structure Hamiltonian representations and lower bound certificates
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Quantum Physics arXiv:2602.05069 (quant-ph) [Submitted on 4 Feb 2026] Title:Near-frustration-free electronic structure Hamiltonian representations and lower bound certificates Authors:Nicholas C. Rubin, Guang Hao Low, A. Eugene DePrince III View a PDF of the paper titled Near-frustration-free electronic structure Hamiltonian representations and lower bound certificates, by Nicholas C. Rubin and 2 other authors View PDF HTML (experimental) Abstract:Hamiltonian representations based on the sum-of-squares (SOS) hierarchy provide rigorous lower bounds on ground-state energies and facilitate the design of efficient classical and quantum simulation algorithms. This work presents a unified framework connecting SOS decompositions with variational two-particle reduced density matrix (v2RDM) theory. We demonstrate that the ``weighted'' SOS ansatz naturally recovers the dual of the v2RDM program, enabling the strict enforcement of symmetry constraints such as particle number and spin. We provide explicit SOS constructions for the Hubbard model and electronic structure Hamiltonians, ranging from spin-free approximations to full rank-2 expansions. We also highlight theoretical connections to block-invariant symmetry shifts. Numerical benchmarks on molecular systems and Iron-Sulfur clusters validate these near frustration-free representations, demonstrating their utility in improving spectral gap amplification and reducing block encoding costs in quantum algorithms. Subjects: Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph) Cite as: arXiv:2602.05069 [quant-ph] (or arXiv:2602.05069v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.05069 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nicholas Rubin [view email] [v1] Wed, 4 Feb 2026 21:42:37 UTC (312 KB) Full-text links: Access Paper: View a PDF of the paper titled Near-frustration-free electronic structure Hamiltonian representations and lower bound certificates, by Nicholas C. Rubin and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: physics physics.chem-ph 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?)