Surrogate Optimization for Quantum Circuits

VAriational quantum Eigensolvers are touted as a near-term algoirthm capable of impacting many applicaitons. However, the potential has yet ot be realized with few claims of quantum advantage and high resource estimates mainly due to the need for optimization in the presence of noise. Finding algorithms and methods capable to improve the convergence is essential to acclerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal we look to use modern approaches recently developed in circuit simulations and stochastic classical optimization that can be combined in a surrogate optimization approach to quantum circuits. Using an approximate state vector simulator, we efficiently calculate an approximate Hessian, fed as an input for a detailed quantum circuit simulator. We demonstrate the capabilities of such an approach with and without sampling noise. We also show that this method outperforms Powell in the precense of quantum circuit shot noise by a factor of 2-4