Ab Initio Molecular Dynamics on Quantum Computers*

Simulation of quantum systems is one of the promising applications of quantum computers. In this work, we are exploring the possibility of simulation of the time evolution of molecular systems on quantum computers using the ab initio molecular dynamics (AIMD) approach. The nuclei are propagated classically on Born-Oppenheimer electronic potential energy surfaces, which are obtained from the solution of the electronic Schrödinger equation using the variational quantum eigensolver (VQE) method. The energy gradients are computed numerically using the Hellmann-Feynman theorem, finite differences, and a correlated sampling technique. Our method does not require additional calculations on a quantum computer. To achieve comparable accuracy, our gradient calculation method requires three to five orders of magnitude fewer measurements than the methods without correlated sampling. AIMD dynamics trajectories are simulated for the H₂ molecule on IBM quantum devices. To the best of our knowledge, it is the first successful attempt to run AIMD on quantum devices. With the increasing quality of quantum hardware, our method can be used for studying larger molecules.