Classical Post-processing for Unitary Block Optimization Scheme to Reduce the Effect of Noise on Optimization of Variational Quantum Eigensolvers

TL;DR

This paper introduces classical post-processing methods, Gaussian Process Regression and Double Robust Optimization plus Rejection, to enhance the robustness and accuracy of the Unitary Block Optimization Scheme in VQE under noisy measurement conditions.

Contribution

It presents novel classical post-processing techniques that significantly improve UBOS performance in noisy environments without extra quantum resources.

Findings

Reduction of final relative error by a factor of three.

Enhanced robustness against measurement noise.

No additional quantum measurement overhead required.

Abstract

Variational Quantum Eigensolvers (VQE) are a promising approach for finding the classically intractable ground state of a Hamiltonian. The Unitary Block Optimization Scheme (UBOS) is a state-of-the-art VQE method which works by sweeping over gates and finding optimal parameters for each gate in the environment of other gates. UBOS improves the convergence time to the ground state by an order of magnitude over Stochastic Gradient Descent (SGD). It nonetheless suffers in both rate of convergence and final converged energies in the face of highly noisy expectation values coming from shot noise. Here we develop two classical post-processing techniques which improve UBOS especially when measurements have large noise. Using Gaussian Process Regression (GPR), we generate artificial augmented data using original data from the quantum computer to reduce the overall error when solving for the improved parameters. Using Double Robust Optimization plus Rejection (DROPR), we prevent outlying data which are atypically noisy from resulting in a particularly erroneous single optimization step thereby increasing robustness against noisy measurements. Combining these techniques further reduces the final relative error that UBOS reaches by a factor of three without adding additional quantum measurement or sampling overhead. This work further demonstrates that developing techniques which use classical resources to post-process quantum measurement results can significantly improve VQE algorithms.