A Study on Quantum Car-Parrinello Molecular Dynamics with Classical Shadows for Resource Efficient Molecular Simulation

TL;DR

This paper enhances quantum Car-Parrinello molecular dynamics (QCPMD) by integrating classical shadows, significantly improving resource efficiency for simulating molecular systems on near-term quantum computers.

Contribution

It introduces the use of classical shadows in QCPMD to estimate forces efficiently, enabling more scalable and resource-effective molecular simulations.

Findings

QCPMD with classical shadows accurately simulates equilibrium states.

The method scales better with the number of molecules.

Numerical results on H2 demonstrate improved efficiency.

Abstract

Ab-initio molecular dynamics (AIMD) is a powerful tool to simulate physical movements of molecules for investigating properties of materials. While AIMD is successful in some applications, circumventing its high computational costs is imperative to perform large-scale and long-time simulations. In recent days, near-term quantum computers have attracted much attentions as a possible solution to alleviate the challenge. Specifically, Kuroiwa et al. proposed a new AIMD method called quantum Car-Parrinello molecular dynamics (QCPMD), which exploits the Car-Parrinello method and Langevin formulation to realize cost-efficient simulations at the equilibrium state, using near-term quantum devices. In this work, we build on the proposed QCPMD method and introduce the classical shadow technique to further improve resource efficiency of the simulations. More precisely, classical shadows are used to estimate the forces of all nuclei simultaneously, implying this approach is more effective as the number of molecules increases. We numerically study the performance of our scheme on the $\text{H}_2$ molecule and show that QCPMD with classical shadows can simulate the equilibrium state. Our results will give some insights into efficient AIMD simulations on currently-available quantum computers.