Representational power of selected neural network quantum states in second quantization

Quantum Physics arXiv:2511.04932 (quant-ph) [Submitted on 7 Nov 2025] Title:Representational power of selected neural network quantum states in second quantization Authors:Zhendong Li, Tong Zhao, Bohan Zhang View a PDF of the paper titled Representational power of selected neural network quantum states in second quantization, by Zhendong Li and 2 other authors View PDF HTML (experimental) Abstract:Neural network quantum states emerge as a promising tool for solving quantum many-body problems. However, its successes and limitations are still not well-understood in particular for Fermions with complex sign structures. Based on our recent work [J. Chem. Theory Comput. 21, 10252-10262 (2025)], we generalizes the restricted Boltzmann machine to a more general class of states for Fermions, formed by product of `neurons' and hence will be referred to as neuron product states (NPS). NPS builds correlation in a very different way, compared with the closely related correlator product states (CPS) [H. J. Changlani, et al. Phys. Rev. B, 80, 245116 (2009)], which use full-rank local correlators. In constrast, each correlator in NPS contains long-range correlations across all the sites, with its representational power constrained by the simple function form. We prove that products of such simple nonlocal correlators can approximate any wavefunction arbitrarily well under certain mild conditions on the form of activation functions. In addition, we also provide elementary proofs for the universal approximation capabilities of feedforward neural network (FNN) and neural network backflow (NNBF) in second quantization. Together, these results provide a deeper insight into the neural network representation of many-body wavefunctions in second quantization. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Chemical Physics (physics.chem-ph) Cite as: arXiv:2511.04932 [quant-ph] (or arXiv:2511.04932v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.04932 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhendong Li [view email] [v1] Fri, 7 Nov 2025 02:24:24 UTC (678 KB) Full-text links: Access Paper: View a PDF of the paper titled Representational power of selected neural network quantum states in second quantization, by Zhendong Li and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: cond-mat cond-mat.str-el 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?)