Determining the ensemble N-representability of Reduced Density Matrices
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Quantum Physics arXiv:2602.06167 (quant-ph) [Submitted on 5 Feb 2026] Title:Determining the ensemble N-representability of Reduced Density Matrices Authors:Ofelia B. Oña, Gustavo E. Massaccesi, Pablo Capuzzi, Luis Lain, Alicia Torre, Juan E. Peralta, Diego R. Alcoba, Gustavo E. Scuseria View a PDF of the paper titled Determining the ensemble N-representability of Reduced Density Matrices, by Ofelia B. O\~na and Gustavo E. Massaccesi and Pablo Capuzzi and Luis Lain and Alicia Torre and Juan E. Peralta and Diego R. Alcoba and Gustavo E. Scuseria View PDF HTML (experimental) Abstract:The N-representability problem for reduced density matrices remains a fundamental challenge in electronic structure theory. Following our previous work that employs a unitary-evolution algorithm based on an adaptive derivative-assembled pseudo-Trotter variational quantum algorithm to probe pure-state N-representability of reduced density matrices [J. Chem. Theory Comput. 2024, 20, 9968], in this work we propose a practical framework for determining the ensemble N-representability of a p-body matrix. This is accomplished using a purification strategy consisting of embedding an ensemble state into a pure state defined on an extended Hilbert space, such that the reduced density matrices of the purified state reproduce those of the original ensemble. By iteratively applying variational unitaries to an initial purified state, the proposed algorithm minimizes the Hilbert-Schmidt distance between its p-body reduced density matrix and a specified target p-body matrix, which serves as a measure of the N-representability of the target. This methodology facilitates both error correction of defective ensemble reduced density matrices, and quantum-state reconstruction on a quantum computer, offering a route for density-matrix refinement. We validate the algorithm with numerical simulations on systems of two, three, and four electrons in both, simple models as well as molecular systems at finite temperature, demonstrating its robustness. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.06167 [quant-ph] (or arXiv:2602.06167v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.06167 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: J. Chem. Theory Comput. 2026, 22, 1, 399-406 Related DOI: https://doi.org/10.1021/acs.jctc.5c01788 Focus to learn more DOI(s) linking to related resources Submission history From: Juan Peralta [view email] [v1] Thu, 5 Feb 2026 20:11:03 UTC (459 KB) Full-text links: Access Paper: View a PDF of the paper titled Determining the ensemble N-representability of Reduced Density Matrices, by Ofelia B. O\~na and Gustavo E. Massaccesi and Pablo Capuzzi and Luis Lain and Alicia Torre and Juan E. Peralta and Diego R. Alcoba and Gustavo E. ScuseriaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)