  Variational quantum eigensolvers are touted as a near-term algorithm capable
of impacting many applications. However, the potential has not yet been
realized, with few claims of quantum advantage and high resource estimates,
especially due to the need for optimization in the presence of noise. Finding
algorithms and methods to improve convergence is important to accelerate 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 developed in circuit simulations and stochastic classical
optimization, which can be combined to form a surrogate optimization approach
to quantum circuits. Using an approximate (classical CPU/GPU) state vector
simulator as a surrogate model, we efficiently calculate an approximate
Hessian, passed as an input for a quantum processing unit or exact circuit
simulator. This method will lend itself well to parallelization across quantum
processing units. We demonstrate the capabilities of such an approach with and
without sampling noise and a proof-of-principle demonstration on a quantum
processing unit utilizing 40 qubits.
