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Abstract 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. 

One of the most fundamental problems that has no efficient solutions on classical computers is simulation of quantum systems. It has been long hypothesized that quantum computing devices are naturally more suitable for this task, but many aspects of practical implementations of such simulations remain unknown. One particularly important kind of these simulations is the simulation of molecular dynamics, i.e. prediction of time evolution for a system of interacting particles. In this work we show how a quantum annealer can be used to carry out such simulations by solving differential equations of motion, on the example of the hydrogen molecule. Although the considered system is simple, our method is well scalable and can be readily applied to more complicated systems as annealers with larger number of qubits become available. Importantly, the method is general and can be used to solve arbitrary systems of ordinary non-linear differential equations, which can be helpful not only in the field of computational chemistry, but in many other fields as well.