Variational Parameter Optimization of Quantum-classical Hybrid Heuristics on Near-term Quantum Computer

Currently available quantum processors are noisy intermediate-scale quantum (NISQ) devices. The variational quantum eigensolver (VQE) is an algorithm that is closer to near-term applicability due to lower quantum hardware requirements. In VQE, trial states with variational parameters are prepared by quantum computers, and the optimal parameters are determined by a classical optimizer. This optimization is known to be an NP-hard problem. In this work, we make a comparison between various gradient-free optimizers in terms of approximation ratio and function evaluations. As a result, we find that COBYLA method is the best to find the approximated solution with a lower number of executions of quantum computers.