This study explores the use of equivariant quantum neural networks (QNN) for generating molecular force fields, focusing on the rMD17 dataset. We consider a QNN architecture based on previous research and point out shortcomings in the parametrization of the atomic environments. These shortcomings limit its expressivity as an interatomic potential and precludes transferability between molecules. We propose a revised QNN architecture that addresses these shortcomings. While both QNNs show promise in force prediction, with the revised architecture showing improved accuracy, they struggle with energy prediction. Further, both QNNs architectures fail to demonstrate a meaningful scaling law of decreasing errors with increasing training data. These findings highlight the challenges of scaling QNNs for complex molecular systems and emphasize the need for improved encoding strategies, regularization techniques, and hybrid quantum-classical approaches.
This study explores the use of equivariant quantum neural networks (QNN) for generating molecular force fields, focusing on the rMD17 dataset. We consider a QNN architecture based on previous research and point out shortcomings in the parametrization of the atomic environments. These shortcomings limit its expressivity as an interatomic potential and precludes transferability between molecules. We propose a revised QNN architecture that addresses these shortcomings. While both QNNs show promise in force prediction, with the revised architecture showing improved accuracy, they struggle with energy prediction. Further, both QNNs architectures fail to demonstrate a meaningful scaling law of decreasing errors with increasing training data. These findings highlight the challenges of scaling QNNs for complex molecular systems and emphasize the need for improved encoding strategies, regularization techniques, and hybrid quantum-classical approaches.
This study explores the use of equivariant quantum neural networks (QNN) for generating molecular force fields, focusing on the rMD17 dataset. We consider a QNN architecture based on previous research and point out shortcomings in the parametrization of the atomic environments, that limits its expressivity as an interatomic potential and precludes transferability between molecules. We propose a revised QNN architecture that addresses these shortcomings. While both QNNs show promise in force prediction, with the revised architecture showing improved accuracy, they struggle with energy prediction. Further, both QNNs architectures fail to demonstrate a meaningful scaling law of decreasing errors with increasing training data. These findings highlight the challenges of scaling QNNs for complex molecular systems and emphasize the need for improved encoding strategies, regularization techniques, and hybrid quantum-classical approaches.
Allegro is a machine learning interatomic potential model designed to predict atomic properties in molecules using E(3) equivariant neural networks. When training this model, there tends to be a trade-off between accuracy and inference time. For this reason, we apply multi-objective hyperparameter optimization to both objectives. Additionally, we experiment with modified architectures by constructing variants of Allegro: one extended with additional classical layers and one incorporating quantum-classical hybrid layers. We evaluate all models on QM9, rMD17-aspirin, rMD17-benzene, and a self-generated dataset of copper-lithium structures. As results, both variants surpass Allegro in force prediction accuracy across multiple datasets. The classical variant consistently improves over the baseline, while the quantum-classical hybrid variant achieves the best overall force prediction accuracy on the Cu-Li dataset, where it was fully optimized, outperforming the classical variant by approximately 13%. Notably, the hybrid variant also achieves competitive results on the remaining datasets despite using hyperparameters transferred from Cu-Li without dataset-specific optimization, suggesting that quantum-classical hybridization is a promising direction for enhancing MLIP architectures.
Within a hybrid quantum mechanics/molecular mechanics approach a small region of a large atomistic system is described quantum mechanically, while the rest of the system is represented by a classical force field. Despite this, the computational cost of the quantum calculation severely limits the accessible simulation and sampling time. Replacing the quantum calculation with a machine learning interatomic potential (MLIP) trained on quantum reference data can greatly increase the accessible simulation time. However, the accuracy and efficiency strongly depend on the specific way in which the MLIP incorporates information about the classical (electrostatic) environment. Here, we demonstrate that existing strategies based purely on features derived from an external electric field fail to distinguish certain environments, ultimately limiting their accuracy. As a solution, we propose an extension to the equivariant TensorNet architecture that mitigates this shortcoming by incorporating classical atoms close to the quantum region into the message-passing scheme, combined with features derived from the electric field for describing the environment farther away. We show that this combination achieves higher accuracy than either approach alone.
Machine-learning force fields provide a promising route for accelerating molecular simulation by replacing expensive quantum-chemical calculations with differentiable models of molecular energies and atomic forces. However, learning accurate and energy-conserving forces remains challenging, especially when the model must capture both global energy trends and local potential-energy gradients from limited data. In this work, we propose a Hybrid Quantum SchNet architecture that integrates variational quantum circuit modules into the continuous-filter SchNet framework. Quantum modules are inserted into the filter generator, atom-wise update, and readout transformations, allowing quantum-enhanced feature mappings to contribute to distance-dependent interactions and atomic energy prediction while preserving the energy-gradient formulation of forces. The model is evaluated on eight MD17 molecular systems using 1000 training configurations per molecule. Compared with energy-only training, joint energy--force supervision substantially improves both energy and force prediction accuracy. Compared with energy-only training, joint energy--force supervision substantially improves both energy and force prediction accuracy. Averaged over the benchmark, the energy MAE decreases from 2.567 to 0.593 kcal mol−1, while the force MAE decreases from 16.340 to 1.540 kcal mol−1 Å−1. Ablation experiments on ethanol further show that the performance of the hybrid model depends on the balance between quantum circuit width, circuit depth, and optimization stability. These results demonstrate that variational quantum circuits can be incorporated into neural force-field architectures and trained end-to-end to improve molecular energy and force prediction.
Abstract Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning (ML) methods have demonstrated impressive performances in predicting accurate values for energy and forces when trained on finite size ensembles generated with ab initio techniques. At the same time, quantum computers have recently started to offer new viable computational paradigms to tackle such problems. On the one hand, quantum algorithms may notably be used to extend the reach of electronic structure calculations. On the other hand, quantum ML is also emerging as an alternative and promising path to quantum advantage. Here we follow this second route and establish a direct connection between classical and quantum solutions for learning neural network (NN) potentials. To this end, we design a quantum NN architecture and apply it successfully to different molecules of growing complexity. The quantum models exhibit larger effective dimension with respect to classical counterparts and can reach competitive performances, thus pointing towards potential quantum advantages in natural science applications via quantum ML.
Machine learning holds fundamental computational significance due to the increasing demand for efficient solutions to complex tasks in data analysis, pattern recognition, and optimization, which are essential for addressing the multifaceted challenges of modern society. As the volume of data proliferates at an unprecedented rate, the need for more powerful machine learning strategies becomes increasingly evident. Quantum neural networks (QNNs) represent an emerging and transformative research field that seeks to harness the unique principles of quantum mechanics to enhance the capabilities of machine learning algorithms. This survey examines various QNN approaches, including fully connected QNNs, quantum convolutional neural networks, equivariant QNNs, quantum Hopfield networks, quantum Boltzmann machines, quantum reservoir computing, and composite networks for quantum reinforcement learning, quantum generative learning, and quantum transfer learning. We summarize the relevant investigations on their performance, including learning accuracy, training time, and resource requirements, etc. Each QNN type has unique strengths and weaknesses, offering diverse solutions for different applications.