Quantum-assisted variational Monte Carlo

TL;DR

This paper introduces a quantum-assisted variational Monte Carlo algorithm that leverages quantum hardware to improve sampling efficiency and convergence in finding ground states of quantum many-body systems, demonstrating advantages over classical methods.

Contribution

The paper adapts the quantum-enhanced Markov chain Monte Carlo algorithm to variational Monte Carlo, showing quantum-assisted proposals can outperform classical ones in specific quantum many-body problems.

Findings

Quantum-assisted proposals have larger spectral gaps.

Reduced autocorrelation times in sampling.

Faster convergence to ground states.

Abstract

Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry. Recent advancements in quantum hardware have opened new avenues for addressing this challenge. Inspired by the quantum-enhanced Markov chain Monte Carlo (QeMCMC) algorithm [Nature, 619, 282-287 (2023)], which was originally designed for sampling the Boltzmann distribution of classical spin models using quantum computers, we introduce a quantum-assisted variational Monte Carlo (QA-VMC) algorithm for solving the ground state of quantum many-body systems by adapting QeMCMC to sample the distribution of a (neural-network) wave function in VMC. The central question is whether such quantum-assisted proposal can potentially offer a computational advantage over classical methods. Through numerical investigations for the Fermi-Hubbard model and molecular systems, we demonstrate that the quantum-assisted proposal exhibits larger absolute spectral gaps and reduced autocorrelation times compared to conventional classical proposals, leading to more efficient sampling and faster convergence to the ground state in VMC as well as more accurate and precise estimation of physical observables. This advantage is especially pronounced for specific parameter ranges, where the ground-state configurations are more concentrated in some configurations separated by large Hamming distances. Our results underscore the potential of quantum-assisted algorithms to enhance classical variational methods for solving the ground state of quantum many-body systems.