# Hybrid Quantum--Classical Machine Learning Potential with Variational Quantum Circuits

arXiv: https://arxiv.org/abs/2508.04098 · HTML: https://mlsanity.com/paper/2508.04098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 72 references that are in the map.
- First posted on arXiv 6 Aug 2025.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning](https://mlsanity.com/paper/1910.06151/) (2019)
- [A Survey on Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead](https://mlsanity.com/paper/2310.10315/) (2023)
- [Directional Message Passing on Molecular Graphs via Synthetic Coordinates](https://mlsanity.com/paper/2111.04718/) (2021)
- [Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation](https://mlsanity.com/paper/2211.08737/) (2022)
- [Robust Dequantization of the Quantum Singular value Transformation and Quantum Machine Learning Algorithms](https://mlsanity.com/paper/2304.04932/) (2023)
- [Efficient Quantum Circuits for Machine Learning Activation Functions including Constant T-depth ReLU](https://mlsanity.com/paper/2404.06059/) (2024)

## Abstract (arXiv)

Quantum algorithms for simulating large and complex molecular systems are still in their infancy, and surpassing state-of-the-art classical techniques remains an ever-receding goal post. A promising avenue of inquiry in the meanwhile is to seek practical advantages through hybrid quantum-classical algorithms, which combine conventional neural networks with variational quantum circuits (VQCs) running on today's noisy intermediate-scale quantum (NISQ) hardware. Such hybrids are well suited to NISQ hardware. The classical processor performs the bulk of the computation, while the quantum processor executes targeted sub-tasks that supply additional non-linearity and expressivity. Here, we benchmark a purely classical E(3)-equivariant message-passing machine learning potential (MLP) against a hybrid quantum-classical MLP for predicting density functional theory (DFT) properties of liquid silicon. In our hybrid architecture, every readout in the message-passing layers is replaced by a VQC. Molecular dynamics simulations driven by the HQC-MLP reveal that an accurate reproduction of high-temperature structural and thermodynamic properties is achieved with VQCs. These findings demonstrate a concrete scenario in which NISQ-compatible HQC algorithm could deliver a measurable benefit over the best available classical alternative, suggesting a viable pathway toward near-term quantum advantage in materials modeling.