We report the first-ever formulation of the molecular dynamics problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and demonstrate its successful solution on a D-Wave quantum annealer. This methodology, named a Quantum Differential Equation (QDE) solver, is applied to propagate trajectories for the vibrational motion of hydrogen molecule, H<sub>2</sub>, in three different energy regimes: nearly harmonic, highly anharmonic, and above dissociation threshold. The results obtained using the D-Wave 2000Q quantum annealer are mutually consistent and quickly converge to the exact solution. Several alternative strategies for such calculations are explored and it is shown that the most accurate result and the best efficiency are obtained by combining quantum annealer with classical post-processing (known as “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.

Classical trajectory simulations on a D-Wave quantum annealer

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