Approximate quantum circuit compilation for proton-transfer kinetics on quantum processors

Proton transfer reactions are fundamental to many chemical and biological systems, where quantum effects such as tunneling, delocalization, and zero-point motion play key kinetic control roles. However, classical methods capable of accurately capturing these phenomena scale prohibitively with system size. Here, we develop and demonstrate quantum computing algorithms based on the Nuclear-Electronic Orbital framework, treating the transferring proton quantum mechanically. We assess the potential of current quantum devices for simulating proton transfer kinetics with high accuracy. We first construct a deep initial ansätze within a truncated orbital space by employing the frozen natural orbital approximation. Then, to balance circuit depth against state fidelity, we implement an adaptive form of approximate quantum compiling. Using resulting circuits at varying compression levels transpiled for the ibm_fez device, we compute barrier heights and delocalised proton densities along the proton transfer pathway using a realistic hardware noise model. We find that, although current quantum hardware introduces significant noise relative to the demanding energy tolerances involved, our approach allows substantial circuit simplification while maintaining energy barrier estimates within 13% of the reference value. Despite present hardware limitations, these results offer a practical means of approximating key circuit segments in near-term devices and early fault-tolerant quantum computing systems.