Correlated Purification for Restoring $N$-Representability in Quantum Simulation

Quantum Physics arXiv:2511.10789 (quant-ph) [Submitted on 13 Nov 2025] Title:Correlated Purification for Restoring $N$-Representability in Quantum Simulation Authors:Yuchen Wang, Irma Avdic, Michael Rose, Lillian I. Payne Torres, Anna O. Schouten, Kevin J. Sung, David A. Mazziotti View a PDF of the paper titled Correlated Purification for Restoring $N$-Representability in Quantum Simulation, by Yuchen Wang and 5 other authors View PDF HTML (experimental) Abstract:Classical shadow tomography offers a scalable route to estimating properties of quantum states, but the resulting reduced density matrices (RDMs) often violate constraints that ensure they represent $N$-electron states -- known as $N$-representability conditions -- because of statistical and hardware noise. We present a correlated purification framework based on semidefinite programming to restore accuracy to these noisy, unphysical two-electron RDMs. The method performs a bi-objective optimization that minimizes both the many-electron energy and the nuclear norm of the change in the measured 2-RDM. The nuclear norm, often employed in matrix completion, promotes low-rank, physically meaningful corrections to the 2-RDM, while the energy term acts as a regularization term that can improve the purity of the ground state. While the method is particularly effective for the ground state, it can also be applied to excited and non-stationary states by decreasing the weight of the energy relative to the error norm. In an application to fermionic shadow tomography of large hydrogen chains, correlated purification yields substantial reductions in both energy and 2-RDM error, achieving chemical accuracy across dissociation curves. This framework provides a robust strategy for tomography in many-body quantum simulations. Subjects: Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph) Cite as: arXiv:2511.10789 [quant-ph] (or arXiv:2511.10789v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.10789 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: David Mazziotti [view email] [v1] Thu, 13 Nov 2025 20:25:34 UTC (995 KB) Full-text links: Access Paper: View a PDF of the paper titled Correlated Purification for Restoring $N$-Representability in Quantum Simulation, by Yuchen Wang and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: physics physics.chem-ph physics.comp-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?)