  Ab initio molecular dynamics (AIMD) is a valuable technique for studying
molecules and materials at finite temperatures where the nuclei evolve on
potential energy surfaces obtained from accurate electronic structure
calculations. In this work, a quantum computer-based AIMD method is presented.
The electronic energies are calculated on a quantum computer using the
variational quantum eigensolver (VQE) method. We compute the energy gradients
numerically using the Hellmann-Feynman theorem, finite differences, and a
correlated sampling technique. Our method only requires additional classical
calculations of electron integrals for each degree of freedom, without any
additional computations on a quantum computer beyond the initial VQE run. To
achieve comparable accuracy, our gradient calculation method requires three to
five orders of magnitude fewer measurements than other brute force methods
without correlated sampling. As a proof of concept, AIMD dynamics simulations
are demonstrated 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
for a chemical system. In addition, we demonstrate the validity of the method
for larger molecules using full configuration interaction (FCI) wave functions.
As quantum hardware and noise mitigation techniques continue to improve, the
method can be utilized for studying larger molecular and material systems.
