  Hybrid variational quantum algorithms, which combine a classical optimizer
with evaluations on a quantum chip, are the most promising candidates to show
quantum advantage on current noisy, intermediate-scale quantum (NISQ) devices.
The classical optimizer is required to perform well in the presence of noise in
the objective function evaluations, or else it becomes the weakest link in the
algorithm. We introduce the use of Gaussian Processes (GP) as surrogate models
to reduce the impact of noise and to provide high quality seeds to escape local
minima, whether real or noise-induced. We build this as a framework on top of
local optimizations, for which we choose Implicit Filtering (ImFil) in this
study. ImFil is a state-of-the-art, gradient-free method, which in comparative
studies has been shown to outperform on noisy VQE problems. The result is a new
method: "GP+ImFil". We show that when noise is present, the GP+ImFil approach
finds results closer to the true global minimum in fewer evaluations than
standalone ImFil, and that it works particularly well for larger dimensional
problems. Using GP to seed local searches in a multi-modal landscape shows
mixed results: although it is capable of improving on ImFil standalone, it does
not do so consistently and would only be preferred over other, more exhaustive,
multistart methods if resources are constrained.
