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

arXiv: https://arxiv.org/abs/2512.05475 · HTML: https://mlsanity.com/paper/2512.05475/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Builds on (most cited first, 19 of 19)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
- [Training-efficient density quantum machine learning](https://mlsanity.com/paper/2405.20237/) (2024)
- [On the Ability of Deep Networks to Learn Symmetries from Data: A Neural Kernel Theory](https://mlsanity.com/paper/2412.11521/) (2024)
- [Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks](https://mlsanity.com/paper/2406.18316/) (2024)
- [3D Scalable Quantum Convolutional Neural Networks for Point Cloud Data Processing in Classification Applications](https://mlsanity.com/paper/2210.09728/) (2022)
- [Resource-efficient equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2410.01252/) (2024)
- [Molecule Graph Networks with Many-body Equivariant Interactions](https://mlsanity.com/paper/2406.13265/) (2024)

## Abstract (arXiv)

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.