Velocity Verlet-based optimization for variational quantum eigensolvers

TL;DR

This paper introduces a velocity Verlet-based optimization method for VQE that improves the efficiency and accuracy of quantum chemistry simulations on near-term quantum computers.

Contribution

It adapts the classical velocity Verlet algorithm to quantum variational optimization, offering a novel approach to enhance VQE performance.

Findings

Achieves chemical accuracy for H2 with fewer circuit evaluations.

Attains lowest final energy for LiH compared to standard optimizers.

Demonstrates potential for high-accuracy quantum chemistry simulations.

Abstract

The Variational Quantum Eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address this challenge. By introducing an inertial "velocity" term, our method efficiently explores complex energy landscapes. We compare its performance against standard optimizers on H$_2$ and LiH molecules. For H$_2$, our method achieves chemical accuracy with fewer quantum circuit evaluations than L-BFGS-B. For LiH, it attains the lowest final energy, demonstrating its potential for high-accuracy VQE simulations.