PERM EQ x GRAPH EQ: Equivariant Neural Networks for Quantum Molecular Learning

2025/12/05 by Saumya Biswas, Biswas, Saumya, Jiten Oswal +1
Computer Science · Materials Science · #68T05 #68T09 #81P68 #Advanced Graph Neural Networks #Artificial Intelligence (cs.AI) #F.2.2 #FOS: Computer and information sciences #FOS: Physical sciences #I.2.6 #I.2.7 #Machine Learning (cs.LG) #Machine Learning in Materials Science #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2512.05475

openalex publication_date 2025/12/05 · openalex created_date 2025/12/09 · openalex updated_date 2026/07/28

Abstract

In hierarchal order of molecular geometry, we compare the performances of Geometric Quantum Machine Learning models. Two molecular datasets are considered: the simplistic linear shaped LiH-molecule and the trigonal pyramidal molecule NH3. Both accuracy and generalizability metrics are considered. A classical equivariant model is used as a baseline for the performance comparison. The comparative performance of Quantum Machine Learning models with no symmetry equivariance, rotational and permutational equivariance, and graph embedded permutational equivariance is investigated. The performance differentials and the molecular geometry in question reveals the criteria for choice of models for generalizability. Graph embedding of features is shown to be an effective pathway to greater trainability for geometric datasets. Permutational symmetric embedding is found to be the most generalizable quantum Machine Learning model for geometric learning.

Citations

• On the Ability of Deep Networks to Learn Symmetries from Data: A Neural Kernel Theory
• Resource-efficient equivariant quantum convolutional neural networks
• Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks
• Molecule Graph Networks with Many-body Equivariant Interactions
• Training-efficient density quantum machine learning
• Can Variational Quantum Algorithms Demonstrate Quantum Advantages? Time Really Matters
• 3D Scalable Quantum Convolutional Neural Networks for Point Cloud Data Processing in Classification Applications
• Representation Theory for Geometric Quantum Machine Learning
• Equivariant quantum circuits for learning on weighted graphs
• Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
• E(n) Equivariant Graph Neural Networks
• Quantum Graph Neural Networks

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