Hybrid quantum-classical architecture outperforms classical variant in force prediction accuracy on copper-lithium dataset, with the approach remaining competitive when transferred to organic-molecule benchmarks
St. Gallen, Switzerland, October 2026: Terra Quantum and Schaeffler Technologies AG & Co. KG announced the publication of joint research in Computational Materials Science (Elsevier). The paper, “Multi-objective optimization and quantum hybridization of equivariant deep learning interatomic potentials”, is available open access in the Computational Materials Science journal, Volume 270, 2026, Article 114742 and on arXiv.
The publication is the scientific outcome of a commercial project between Terra Quantum and Schaeffler. The research investigates modifications to the Allegro machine learning interatomic potential (MLIP) model, a class of model trained to predict energies and forces of molecular systems, reducing the computational cost of energy calculations while approaching DFT accuracy. The paper constructs variants of the Allegro architecture by adding either classical multi-layer perceptron (MLP) layers or quantum-classical hybrid layers, and evaluates these on four datasets including a self-generated copper-lithium dataset developed for the Schaeffler collaboration.
Results: Hybrid Quantum Architecture on the Cu-Li Dataset
Both architectural variants, classical and hybrid quantum, surpass the team's own retrained Allegro baseline in force prediction accuracy on the datasets where forces were modeled (copper-lithium, aspirin, benzene). Copper-lithium was the only dataset on which the hybrid variant was fully optimized (on force accuracy); there it achieves the best force prediction accuracy, outperforming the classical variant by approximately 13%. “This result demonstrates that quantum-classical hybridization can deliver measurable improvements in force prediction accuracy on an industrial inorganic materials system,” said Dr. Alexey Melnikov, Global Director of Quantum AI at Terra Quantum.
Notably, the hybrid variant also achieves competitive results on the remaining datasets (QM9, rMD17-aspirin, and rMD17-benzene) even though its quantum-specific hyperparameters were carried over from copper-lithium rather than re-tuned for each dataset. The authors note this as evidence that “quantum-classical hybridization is a promising direction for enhancing MLIP architectures.” Dr. Melnikov added: “What is particularly encouraging is that the hybrid variant stays competitive on the other datasets even without dataset-specific optimization, suggesting the approach is worth pursuing beyond the system it was trained on.”
The copper-lithium dataset used in the study is proprietary and self-generated: 11,635 DFT-calculated structures of copper and lithium atoms, including surfaces, interfaces, vacancies, and melt-quench configurations, produced specifically for this industrial collaboration. “Schaeffler is committed to advancing computational methods in materials research,” said Dr. Joanna Procelewska of Schaeffler Technologies. “This work has produced scientifically validated results on a system that is directly relevant to our industrial applications. We are pleased to see it recognized through peer review.”
About the Research
The paper benchmarks the Allegro model and its variants across four datasets: QM9 (organic molecules), rMD17-aspirin, rMD17-benzene, and the proprietary Cu-Li dataset. The quantum-classical hybrid architecture incorporates Quantum Depth-Infused (QDI) layers. Supplementary analysis covers quantum circuit properties including redundancy (ZX calculus), trainability (Fisher information), and expressivity (Fourier analysis).
The full author list spans Terra Quantum, Schaeffler Technologies, Leiden University (Netherlands), University of Jyväskylä (Finland), and the Indian Institute of Science (IISc) Bengaluru (India): G. Laskaris, D. Morozov, D. Tarpanov, A. Seth, J. Procelewska, G. Sai Gautam, A. Sagingalieva, R. Brasher, A. Melnikov.
Publication: Computational Materials Science, Volume 270, 2026, Article 114742