  In this work we demonstrate a practical prospect of using quantum annealers
for simulation of molecular dynamics. A methodology developed for this goal,
dubbed Quantum Differential Equations (QDE), is applied to propagate classical
trajectories for the vibration of the hydrogen molecule in several regimes:
nearly harmonic, highly anharmonic, and dissociative motion. The results
obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly
converge to the analytical reference solution. Several alternative strategies
for such calculations are explored and it was found that the most accurate
results and the best efficiency are obtained by combining the quantum annealer
with classical post-processing (greedy algorithm). Importantly, the QDE
framework developed here is entirely general and can be applied to solve any
system of first-order ordinary nonlinear differential equations using a quantum
annealer.
