A quantum computing implementation of nuclearelectronic orbital (NEO) theory: Toward an exact pre-Born–Oppenheimer formulation of molecular quantum systems.

This article presents a resource-efficient quantum algorithm for simulating molecular systems by treating both electrons and selected light nuclei quantum mechanically within the Nuclear–Electronic Orbital (NEO) framework on near-term quantum computers. The authors develop and implement tailored wave function Ansätze, including a modified Unitary Coupled Cluster (NEOUCC) and hardware-efficient parameterizations, alongside advanced parameter initialization and qubit reduction techniques exploiting molecular symmetries to reduce computational resources. Benchmark applications to the hydrogen molecule and malonaldehyde demonstrate that the approach achieves ground state energies and electron–nuclear entanglement entropies in close agreement with classical NEO full configuration interaction and complete active space configuration interaction methods, with errors below 10⁻⁶ hartree. The study highlights the significance of electron–nuclear correlation effects and shows that the proposed quantum algorithm can capture nuclear quantum phenomena such as proton transfer barriers, offering a promising pathway toward scalable quantum simulations of electron–nuclear dynamics beyond the Born–Oppenheimer approximation.