  The theoretical investigation of non-adiabatic processes is hampered by the
complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer
approximation. Classically, the simulation of such reactions is limited by the
unfavourable scaling of the computational resources as a function of the system
size. While quantum computing exhibits proven quantum advantage for the
simulation of real-time dynamics, the study of quantum algorithms for the
description of non-adiabatic phenomena is still unexplored. In this work, we
propose a quantum algorithm for the simulation of fast non-adiabatic chemical
processes together with an initialization scheme for quantum hardware
calculations. In particular, we introduce a first-quantization method for the
time evolution of a wavepacket on two coupled harmonic potential energy
surfaces (Marcus model). In our approach, the computational resources scale
polynomially in the system dimensions, opening up new avenues for the study of
photophysical processes that are classically intractable.
