Improved precision scaling for simulating coupled quantum-classical dynamics

TL;DR

This paper introduces a quantum simulation method that significantly improves the precision of coupled quantum-classical dynamics, enabling efficient estimation of thermodynamic properties with super-polynomial advantages.

Contribution

It presents a novel quantum algorithm leveraging Koopman-von Neumann mechanics to simulate classical particles coupled with quantum systems more efficiently than classical methods.

Findings

Achieves super-polynomial precision scaling in quantum simulations

Enables simulation of classical particles in different thermodynamic ensembles

Reduces measurement and computation overheads compared to classical approaches

Abstract

We present a super-polynomial improvement in the precision scaling of quantum simulations for coupled classical-quantum systems in this paper. Such systems are found, for example, in molecular dynamics simulations within the Born-Oppenheimer approximation. By employing a framework based on the Koopman-von Neumann formulation of classical mechanics, we express the Liouville equation of motion as unitary dynamics and utilize phase kickback from a dynamical quantum simulation to calculate the quantum forces acting on classical particles. This approach allows us to simulate the dynamics of these classical particles without the overheads associated with measuring gradients and solving the equations of motion on a classical computer, resulting in a super-polynomial advantage at the price of increased space complexity. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles, enabling the estimation of thermodynamic properties from the prepared probability density.