Adaptive Observation Cost Control for Variational Quantum Eigensolvers

TL;DR

This paper introduces SubsCoRe, an adaptive measurement shot control method for VQE that uses Gaussian process surrogates to reduce observation costs while maintaining optimization accuracy.

Contribution

The paper presents a novel adaptive cost control approach for SMO in VQE, leveraging Gaussian processes to minimize measurement shots and improve efficiency.

Findings

SubsCoRe reduces measurement shot requirements significantly.

It outperforms existing state-of-the-art methods.

The approach guarantees optimization accuracy with fewer observations.

Abstract

The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise -- one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. The adaptive cost control is performed by first setting the required accuracy according to the progress of the optimization, and then choosing the minimum number of measurement shots and their distribution such that the required accuracy is satisfied. We demonstrate that SubsCoRe significantly improves the efficiency of SMO, and outperforms the state-of-the-art methods.