Classical postprocessing for the unitary block-optimization scheme to reduce the effect of noise on the optimization of variational quantum eigensolvers

Variational quantum eigensolvers (VQEs) 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 that 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. 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 postprocessing techniques that improve UBOS especially when measurements have large shot noise. Using Gaussian process regression, 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, 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 3 without adding additional quantum measurement or sampling overhead. This work further demonstrates that developing techniques that use classical resources to postprocess quantum measurement results can significantly improve VQE algorithms.