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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.

 

Aims. We present new calculations of collision cross sections for state-to-state transitions between the rotational states in an H 2 O + H 2 O system, which are used to generate a new database of collisional rate coefficients for cometary and planetary applications. Methods. Calculations were carried out using a mixed quantum-classical theory approach that is implemented in the code MQCT. The large basis set of rotational states used in these calculations permits us to predict thermally averaged cross sections for 441 transitions in para- and ortho-H 2 O in a broad range of temperatures. Results. It is found that all state-to-state transitions in the H 2 O + H 2 O system split into two well-defined groups, one with higher cross-section values and lower energy transfer, which corresponds to the dipole-dipole driven processes. The other group has smaller cross sections and higher energy transfer, driven by higher-order interaction terms. We present a detailed analysis of the theoretical error bars, and we symmetrized the state-to-state transition matrixes to ensure that excitation and quenching processes for each transition satisfy the principle of microscopic reversibility. We also compare our results with other data available from the literature for H 2 O + H 2 O collisions.