Ab Initio Molecular Dynamics on Quantum Computers

Abstract

One of the most promising applications of quantum computing is the quantum-chemical calculation of molecular properties [1,2,3]. On near-term quantum computers, the electronic ground state wave function of a given molecule can be found by minimizing the expectation value of the molecular Hamiltonian. One common algorithm to perform this minimization is called the variational quantum eigensolver [4]. Arbitrary operators can then be evaluated on the electronic wavefunction on the quantum computer to determine molecular properties like energy, electric dipole moment or magnetization. The molecular forces can thus be obtained by evaluating the corresponding operators on the quantum computer [5]. Based on this, a hybrid quantum-classical algorithm can be formulated for the simulation of ground-state Born-Oppenheimer dynamics [5,6]. The algorithm consists of three repeating steps: firstly, on the quantum computer, obtain the ground state wavefunction of a molecule in a given nuclear configuration. Secondly, on the quantum computer, evaluate the nuclear force operators. Thirdly, on a classical computer, integrate Newtons equation of motion for the nuclei. We implemented the proposed algorithm and applied molecular dynamics simulations for single lithium hydride, hydrogen and water molecules. The quantum computation is performed on a noiseless statevector simulator. The infrared spectra derived from the simulations achieve a good agreement with experimental data. Our results demonstrate the viability of hybrid quantum-classical simulation of accurate Born-Oppenheimer dynamics. While current quantum computers are too limited to demonstrate an advantage compared to classical methods, in the future they may become a powerful tool for molecular dynamics. Literature: [1] P. J. J. O’Malley et al., Phys. Rev. X. 6, 031007 (2016). [2] O. Higgott, D. Wang, S. Brierley, Quantum. 3, 156 (2019). [3] S. McArdle, A. Mayorov, X. Shan, S. Benjamin, X. Yuan, Chem. Sci. 10, 5725–5735 (2019). [4] A. Peruzzo et al., Nat Commun. 5, 4213 (2014). [5] T. E. O’Brien et al., Phys. Rev. Research. 4, 043210 (2022). [6] D. A. Fedorov, M. J. Otten, S. K. Gray, Y. Alexeev, J. Chem. Phys. 154, 164103 (2021).