Efficient Parabolic Optimisation Algorithm for Adaptive VQE Implementations

Abstract

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. 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. We then continue to benchmark the parabolic optimiser against COBYLA for various implementations of VQE. We found that the parabolic optimizer consistently outperforms traditional optimization algorithms in multiple VQE implementations. Specifically, we show that the parabolic optimizer requires fewer quantum experiments compared to COBYLA while producing circuits with a similar amount of CNOTs.