Machine-Learning-Enhanced Optimization of Noise-Resilient Variational Quantum Eigensolvers

TL;DR

This paper explores how machine learning, specifically Gaussian Processes and Bayesian Optimization, can improve the performance of Variational Quantum Eigensolvers on noisy quantum hardware, with promising simulation results.

Contribution

It introduces an enhanced optimization algorithm for VQEs using machine learning techniques and evaluates its robustness against hardware noise and error mitigation strategies.

Findings

GP-enhanced algorithms outperform state-of-the-art baselines

Hardware noise impacts the algorithm's performance

Simulations validate the approach's potential for real hardware

Abstract

Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications, including lattice field theory. However, the inherent noise of Noisy Intermediate-Scale Quantum (NISQ) devices poses a significant challenge for running VQEs as these algorithms are particularly susceptible to noise, e.g., measurement shot noise and hardware noise. In a recent work, it was proposed to enhance the classical optimization of VQEs with Gaussian Processes (GPs) and Bayesian Optimization, as these machine-learning techniques are well-suited for handling noisy data. In these proceedings, we provide additional insights into this new algorithm and present further numerical experiments. In particular, we examine the impact of hardware noise and error mitigation on the algorithm's performance. We validate the algorithm using classical simulations of quantum hardware, including hardware noise benchmarks, which have not been considered in previous works. Our numerical experiments demonstrate that GP-enhanced algorithms can outperform state-of-the-art baselines, laying the foundation for future research on deploying these techniques to real quantum hardware and lattice field theory setups.