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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.

 

A theoretical approach is developed for the description of all possible recombination pathways in the ozone forming reaction, without neglecting any process a priori, and without decoupling the individual pathways one from another. These pathways become physically distinct when a rare isotope of oxygen is introduced, such as 18O, which represents a sensitive probe of the ozone forming reaction. Each isotopologue of O3 contains two types of physically distinct entrance channels and two types of physically distinct product wells, creating four recombination pathways. Calculations are done for singly and doubly substituted isotopologues of ozone, eight rate coefficients total. Two pathways for the formation of asymmetric ozone isotopomer exhibit rather different rate coefficients, indicating large isotope effect driven by ΔZPE-difference. Rate coefficient for the formation of symmetric isotopomer of ozone (third pathway) is found to be in between of those two, while the rate of insertion pathway is smaller by two orders of magnitude. These trends are in good agreement with experiments, for both singly and doubly substituted ozone. The total formation rates for asymmetric isotopomers are found to be somewhat larger than those for symmetric isotopomers, but not as much as in the experiment. Overall, the distribution of lifetimes is found to be very similar for the metastable states in symmetric and asymmetric ozone isotopomers. 

Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for O + O collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.