Fundamental Research on Applying Artificial Bee Colony Algorithm to an Optimizer in Variational Quantum Eigensolver

The variational quantum eigensolver (VQE), a hybrid algorithm combining quantum and classical computing, has attracted significant interest. As an optimizer for VQE, gradient-based methods are frequently used. However, in the presence of complex optimization landscapes, these methods may struggle to search for a globally optimal solution. In this study, we applied the artificial bee colony (ABC) algorithm as an optimizer for VQE, which is a robust swarm intelligence for the optimization of high-dimensional functions. We conducted experiments to investigate the effectiveness of the ABC algorithm in solving number partitioning problems (NPPs) of 4, 5, 6, and 8 sizes. The results showed that an ansatz with fewer blocks yielded superior results for NPPs of these sizes. In this context, “block" refers to a pair of entanglement and rotation layers. The parameters related to the local search in the ABC algorithm, which is the number of iterations to abandon, should be increased in the quantum circuit used in this study. Additionally, the population size should be increased in accordance with the size of the problem to be solved. The objective of this research is to contribute to the selection of optimizers for VQE, with a focus on the problem to be solved, and to contribute to the improvement of VQE performance, which has been a significant area of interest in the noisy intermediate-scale quantum era.