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

TL;DR

The paper addresses improving generalization in quantum learning for molecular geometry by leveraging symmetries. It compares four symmetry-aware QML variants against a classical baseline on PSI4-derived LiH and NH3 data, using graph embeddings and a two-phase training regime with cross-validation. The key finding is that graph-permutational equivariance yields superior generalization for geometry-heavy problems, approaching classical performance in some cases, while non-equivariant approaches underperform. These results guide the design of symmetry-aware quantum architectures for quantum chemistry tasks and point toward potential quantum advantage with efficient parameter usage.

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.

Figures (9)

• Figure 1: Training of the four methods with $LiH$-data. All four methods use multi-phase training and/or adapting weights of energy and force in the cost function.
• Figure 2: Energy and force predictions for the $LiH$-molecular data using the four methods.
• Figure 3: Performance of $LiH$-training Cross Validation: Energy and Force $R^2$ and MAE.
• Figure 4: Generalizability metrics of $LiH$-training Cross Validation: Energy and Force generalizability, consistency, and stability.
• Figure 5: A Spider or Web chart for $LiH$: energy $R^2$, mean force $R^2$, energy consistency (inverted), force consistency(inverted), and energy stability(inverted).