A Charge-Consistent Long-Range Machine-Learned Interatomic Potential Compatible with Quantum Linear System Algorithms

Abstract Charge equilibration in machine-learned interatomic potentials (MLIPs) requires repeatedly solving linear systems, providing a promising target for quantum linear-system algorithms (QLSAs). However, conventional electronegativity equalization schemes suffer from spurious fractional charges between neutral fragments at large separations. To address this limitation, we incorporate atom-condensed Kohn–Sham density functional theory approximated to second order (ACKS2) into a long-range equivariant neural-network MLIP. Across benchmark systems, the ACKS2-based model improves energy, force, and charge predictions. At a molecule–metal interface, ACKS2 restores molecular fragments to near-neutral charge states upon separation while preserving local charge redistribution near adsorption. Because ACKS2 charge equilibration reduces to solving a linear system, the classical solver can be directly replaced with the Harrow–Hassidim–Lloyd algorithm during inference, demonstrating compatibility with quantum linear-system solvers. These results indicate that ACKS2 provides a promising framework for charge-aware MLIPs and highlight a potential pathway toward atomistic simulations based on QLSAs.