  In this paper, we propose a cost-reduced method for finite-temperature
molecular dynamics on a near-term quantum computer, Quantum Car-Parrinello
molecular dynamics (QCPMD). One of the most promising applications of near-term
quantum computers is quantum chemistry. It has been expected that simulations
of molecules via molecular dynamics can be also efficiently performed on
near-term quantum computers by applying a promising near-term quantum algorithm
of the variational quantum eigensolver (VQE). However, this method may demand
considerable computational costs to achieve a sufficient accuracy, and
otherwise, statistical noise can significantly affect the results. To resolve
these problems, we invent an efficient method for molecular time evolution
inspired by Car-Parrinello method. In our method, parameters characterizing the
quantum state evolve based on equations of motion instead of being optimized.
Furthermore, by considering Langevin dynamics, we can make use of the intrinsic
statistical noise. As an application of QCPMD, we propose an efficient method
for vibrational frequency analysis of molecules in which we can use the results
of the molecular dynamics calculated by QCPMD. Numerical experiments show that
our method can precisely simulate the Langevin dynamics at the equilibrium
state, and we can successfully predict a given molecule's eigen frequencies.
Furthermore, in the numerical simulation, our method achieves a substantial
cost reduction compared with molecular dynamics using the VQE. Our method
achieves an efficient computation without using widely employed method of the
VQE. In this sense, we open up a new possibility of molecular dynamics on
near-term quantum computers. We expect our results inspire further invention of
efficient near-term quantum algorithms for simulation of molecules.
