(supported by NSF, in collaboration with Los Alamos National Laboratory)

One of the long-thought applications of quantum computers is to simulate quantum systems, such as molecules and materials at the atomistic scale. Several algorithms were recently proposed for the calculations of molecular electronic structure (called *quantum chemistry*) using either gate-based quantum computers with only a few tens of qubits, such as Sycamore or IBM Q-machines, or using quantum annealers with a larger number of qubits, such as the D-Wave systems. Another essential component of chemical modeling is the propagation of the equations of motion for constituent atoms in time and space (*e.g.*, along the reaction path), called *molecular dynamics*. For over 50 years, molecular dynamics simulations have played a pivotal role not only in guiding and analyzing experiments, but also as an interdisciplinary computational tool that is able to reach far beyond experimental conditions. Molecular dynamics is indispensable for a wide variety of research topics, but only a few attempts have been made so far to harness the power of quantum computing for the benefit of molecular dynamics simulations.

We were among the first to explore this opportunity: A few years ago, we developed a new method (named QAE) to solve, on a quantum annealer, the problem of quantum vibrational dynamics as an eigenvalue problem, and, successfully implemented this algorithm using the actual quantum hardware (D-Wave annealer at LANL) to compute the *vibrational states* of O2 and O3 molecules. Later, this method was extended to compute the properties of *quantum scattering resonances* above the dissociation threshold (these metastable states play a central role in *recombination reactions*, such as ozone formation in the Earth’s stratosphere: O + O2 → O3). More recently, we developed another algorithm (named QDE, see Fig. 1) and successfully carried out the first ever molecular dynamics simulations on a quantum annealer, to propagate trajectories for the *vibrational motion* of atoms in the H2 molecule in various energy regimes, including large-amplitude anharmonic vibrations and *bond breaking* (i.e., dissociation reaction H2 + *bath gas* → H + H).

These pioneering proof-of-principle calculations are still restricted to small molecules, such as diatomic and triatomic systems, and are done in a hybrid quantum/classical fashion, when only a part of the overall algorithm is run on a present-day quantum device. However, they represent the first step toward the development of new algorithms, exploration of larger molecules, and modelling of more complex processes that may become possible using the last generation quantum computers, such as D-Wave’s Advantage.

Fig. 1: Schematic representation of the workflow in our QDE algorithm for simulation of molecular dynamics on a quantum annealer, going from the potential function to QUBO matrix, to its minimization on quantum device, to making a timestep along the trajectory, and then repeating the cycle.

1. I. Gayday, D. Babikov, A. Teplukhin, B. K. Kendrick, S. M. Mniszewski, Y. Zhang, S. Tretiak, P. A. Dub, “Molecular dynamics on quantum annealers” Sci. Reports 12, 16824 (10 pages), 2022.

2. A. Teplukhin, B. Kendrick and D. Babikov, “Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances”, Phys. Chem. Chem. Phys. 22, 26136-26144, 2020.

3. A. Teplukhin, B. Kendrick and D. Babikov, “Calculation of molecular vibrational spectra on a quantum annealer”, J. Chem. Theory Comput. 15, 4555-4563, 2019.

4. D. Shyshlov and D. Babikov, “Computational study of cold ions trapped in a double-well potential”, Mol. Phys. 117, 1912-1925, 2019.