  Computational chemistry is one of the most promising applications of quantum
computing, mostly thanks to the development of the Variational Quantum
Eigensolver (VQE) algorithm. VQE is being studied extensively and numerous
optimisations of VQE's sub-processes have been suggested, including the
encoding methods and the choice of excitations. Recently, adaptive methods were
introduced that apply each excitation iteratively. When it comes to adaptive
VQE, research is focused on the choice of excitation pool and the strategies
for choosing each excitation. Here we focus on a usually overlooked component
of VQE, which is the choice of the classical optimisation algorithm. We
introduce the parabolic optimiser that we designed specifically for the needs
of VQE. This includes both an 1-D and an n-D optimiser that can be used either
for adaptive or traditional VQE implementations. We then continue to benchmark
the parabolic optimiser against Nelder-Mead for various implementations of VQE.
We found that the parabolic optimiser performs significantly better than
traditional optimisation methods, requiring fewer CNOTs and fewer quantum
experiments to achieve a given energy accuracy.
