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

TL;DR

This paper evaluates various equivariant quantum machine learning models on molecular datasets, demonstrating that graph-embedded permutational equivariance offers superior generalizability and trainability for geometric learning tasks.

Contribution

It introduces and compares different symmetry-equivariant quantum models, highlighting the effectiveness of graph-embedded permutational equivariance for molecular learning.

Findings

Graph embedding improves trainability on geometric datasets.

Permutational symmetric embedding shows highest generalizability.

Equivariant models outperform non-equivariant counterparts.

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.