Accelerating Noisy VQE Optimization with Gaussian Processes

TL;DR

This paper introduces a Gaussian Process-based framework to enhance the efficiency and accuracy of noisy variational quantum eigensolver (VQE) optimization, especially on NISQ devices, by reducing noise impact and improving convergence.

Contribution

The paper presents a novel GP+ImFil method that improves noisy VQE optimization by integrating Gaussian Processes with local gradient-free optimization, outperforming standalone methods in certain scenarios.

Findings

GP+ImFil finds results closer to the global minimum with fewer evaluations.

The method performs particularly well on larger, high-dimensional problems.

Mixed results in multi-modal landscapes suggest resource trade-offs for seed-based optimization.

Abstract

Hybrid variational quantum algorithms, which combine a classical optimizer with evaluations on a quantum chip, are the most promising candidates to show quantum advantage on current noisy, intermediate-scale quantum (NISQ) devices. The classical optimizer is required to perform well in the presence of noise in the objective function evaluations, or else it becomes the weakest link in the algorithm. We introduce the use of Gaussian Processes (GP) as surrogate models to reduce the impact of noise and to provide high quality seeds to escape local minima, whether real or noise-induced. We build this as a framework on top of local optimizations, for which we choose Implicit Filtering (ImFil) in this study. ImFil is a state-of-the-art, gradient-free method, which in comparative studies has been shown to outperform on noisy VQE problems. The result is a new method: "GP+ImFil". We show that when noise is present, the GP+ImFil approach finds results closer to the true global minimum in fewer evaluations than standalone ImFil, and that it works particularly well for larger dimensional problems. Using GP to seed local searches in a multi-modal landscape shows mixed results: although it is capable of improving on ImFil standalone, it does not do so consistently and would only be preferred over other, more exhaustive, multistart methods if resources are constrained.