Density matrix based perturbative corrections for improved quantum simulation accuracy

TL;DR

This paper introduces density matrix purification and perturbative correction techniques as error mitigation methods for noisy quantum computers, enhancing the accuracy of quantum simulations like VQE with minimal classical overhead.

Contribution

The authors develop a post-processing scheme using density matrix purification and perturbative corrections to improve quantum simulation accuracy without significant additional resources.

Findings

Achieved chemically-accurate ground state energies for alkali metal hydrides.

Enhanced simulation accuracy and reduced measurement variation.

Applicable to various quantum algorithms with minimal classical computation.

Abstract

We present error mitigation (EM) techniques for noisy intermediate-scale quantum computers (QC) based on density matrix purification and perturbative corrections to the target energy. We incorporate this scheme into the variational quantum eigensolver (VQE) and demonstrate chemically-accurate ground state energy calculations of various alkali metal hydrides using IBM quantum computers. Both the density matrix purification improvements and the perturbative corrections require only meager classical computational resources, and are conducted exclusively as post-processing of the measured density matrix. The improved density matrix leads to better simulation accuracy at each step of the variational optimization, resulting in a better input into the next optimization step without additional measurements. Adding perturbative corrections to the resulting energies further increases the accuracy, and decreases variation between consecutive measurements. These EM schemes allow for previously unavailable levels of accuracy over remote QC resources.