Improved Resource Allocation in Variational Quantum Algorithms

Estimation of quantum observables is a fundamental task in quantum mechanics. Quantum simulation algorithms targeted towards estimating ground state energies or performing quantum dynamics use estimation of quantum observables as a subroutine. Given the probabilistic nature of quantum mechanics, the estimation procedure involves repeated measurements and statistical inference. As the size of physical systems of interest increases, the estimation becomes more resource intensive. Building upon recent works on utilizing adaptive measurements and Bayesian inference, we propose a methodology that focuses on designing better priors for estimating the expectation values and the associated uncertainties while optimizing for the quantum and classical computing resources. Our proposed priors contain an additional degree of freedom, and optimizing over it helps to reduce the bias incurred due to the mis-match between the prior and the true distribution. We apply our method to compute the expectation values of static parameterized quantum circuits and the expectation values of quantum states encountered during variational quantum eigensolver iterations.