Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows

TL;DR

This paper explores an improved quantum Monte Carlo algorithm combining quantum and classical methods, using Matchgate shadows to enhance efficiency and noise robustness in electronic structure calculations, but faces scalability challenges due to classical post-processing costs.

Contribution

It introduces a Matchgate shadows-based QC-QMC algorithm that removes exponential scaling and demonstrates noise robustness, advancing quantum chemistry simulations.

Findings

Matchgate shadows remove exponential post-processing bottleneck.

The algorithm shows inherent noise robustness on quantum hardware.

Classical post-processing remains computationally intensive, limiting scalability.

Abstract

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by Huggins et al.[1] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling post-processing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [2], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical post-processing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm.