Quantum algorithm for Ewald summation based computation of long-range electrostatics

TL;DR

This paper introduces a quantum-classical algorithm leveraging Quantum Fourier Transform to efficiently compute long-range electrostatic interactions in molecular systems, promising significant speedups for molecular dynamics simulations.

Contribution

It presents a novel quantum algorithm for Ewald summation that reduces complexity and enables quantum-enhanced molecular simulations.

Findings

Quantum algorithm complexity is $N \, ext{log} \, M$

Quantum advantage when grid points $M^3$ exceed charges $N$

Numerical error is less than $10^{-3}$

Abstract

In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate computation of the Coulomb electrostatic energy for a system of point charges. The algorithm employs the Ewald method based decomposition of electrostatic energy into several energy terms, of which the "Fourier component" (long-range electrostatics) computed on a quantum device, utilizing the power of Quantum Fourier Transform (QFT). We demonstrate that the algorithm complexity is $N \log M$ and that the quantum advantage for a system of point charges in the three-dimensional space is achieved when the number of grid points $M^3$ exceeds the number of charges $N$. The numerical error is small $<10^{-3}$. The algorithm can be implemented to run the all-atom Molecular Dynamics simulations on a quantum device requiring 15 qubits, thereby expanding the scope of applications of QFT-based methods to computational chemistry and biophysics.