Nonadiabatic Molecular Dynamics with Quantum Algorithms.

Investigating ultrafast electron-nuclear dynamics in molecules requires robust theoretical methods that offer predictive capabilities beyond interpretation purposes. However, the vast number of electronic and nuclear degrees of freedom often prevents an accurate description of chemical systems on classical computers. To address these challenges, hybrid approaches combining quantum and classical computing can leverage the strengths of both to enhance the computational efficiency and fully exploit hardware capabilities. In this work, we perform excited-state molecular dynamics simulations of the formaldimine molecule by combining the surface hopping nonadiabatic molecular dynamics technique with quantum algorithms. We replace conventional electronic energy and overlap calculations with the variational quantum deflation (VQD) algorithm and the Hadamard test, respectively, employing a configuration state function (CSF) spin-restricted ansatz. Finally, we evaluate the accuracy and feasibility of three different gradient calculation approaches integrated with the quantum computing components, demonstrating the advantages of an analytical gradient method over finite difference approaches for hybrid quantum-classical integration.