Bayesian Optimization of Variational Quantum Eigensolvers

Abstract

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm used to find the ground state of a Hamiltonian using variational methods. It has a wide range of potential applications, from quantum chemistry to lattice gauge theories in the Hamiltonian formulation. VQE relies on quantum computers to evaluate the energy of the system in terms of circuit parameters, and it minimizes this parametrized energy with a classical optimization routine. This work describes a Bayesian optimization (BO) algorithm specifically designed to minimize the parametrized energy obtained with a quantum computer. BO based on Gaussian process regression (GPR) is an algorithm for finding the global minimum of a black-box cost function, e.g. the energy, with a very low number of iterations even when using data affected by statistical noise. Furthermore, the GPR procedure developed for this work proved to be very versatile as we also used it to compute discrete integral transforms of noisy data. In particular, this procedure was used to reconstruct parton distribution functions from lattice QCD data.