Dresden 2026 – scientific programme
Parts | Days | Selection | Search | Updates | Downloads | Help
TT: Fachverband Tiefe Temperaturen
TT 23: Correlated Electrons – Poster I
TT 23.22: Poster
Monday, March 9, 2026, 18:00–20:00, P1
Polynomial Neural Networks in Quantum Many-Body Physics — •Ashish Yashwanth Kangen1,2 and Werner Dobrautz1,2,3,4 — 1Technical University Dresden, 01069 Dresden, Germany — 2Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig, 01069 Dresden, Germany — 3Center for Advanced Systems Understanding, 02826 Görlitz, Germany — 4Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
Polynomial neural networks were originally derived by applying tensor decompositions to high-order weight tensors. This derivation yields a model architecture that is inherently non-linear through Hadamard products, effectively eliminating the need for standard, tensor-unfriendly activation functions like ReLU.
In this work, we investigate the utility of this architecture within the context of quantum many-body physics and chemistry. We demonstrate that the algebraic properties of these polynomial expansions allow them to serve as robust, activation-free representations of complex quantum correlations. We explore two specific applications: (1) as a standalone wave function ansatz, which can be optimised via both deterministic Density Matrix Renormalization Group sweeps and Variational Monte Carlo, and (2) as a Jastrow correlation factor within the Transcorrelated approach for Quantum Chemistry, trainable via standard gradient-based machine learning optimisation. This framework suggests that the tensor structure underlying polynomial networks offers a flexible and numerically stable bridge between classical deep learning and quantum simulation.
Keywords: Neural Quantum States; Correlated Systems; Transcorrelated Method; Variational Monte Carlo; DMRG