The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently a quantum approximate Bayesian optimization algorithm (QABOA) that includes two mixers was developed, where surrogate-based Bayesian optimization is applied to improve the sampling efficiency of the classical optimizer. A continuous-time quantum walk mixer is used to enhance exploration, and the generalized Grover mixer is also applied to improve exploitation. In this paper, an extension of QABOA is proposed to further improve its searching efficiency. The searching efficiency is enhanced through two aspects. First, two mixers, including one for exploration and the other for exploitation, are applied in an alternating fashion. Second, uncertainty of the quantum circuit is quantified with a new quantum Mat\'ern kernel based on the kurtosis of the basis state distribution, which increases the chance of obtaining the optimum. The proposed new two-mixer QABOA$'$s with and without uncertainty quantification are compared with three single-mixer QABOA$'$s on five discrete and four mixed-integer problems. The results show that the proposed two-mixer QABOA with uncertainty quantification has the best performance in efficiency and consistency for five out of the nine tested problems. The results also show that QABOA with the generalized Grover mixer performs the best among the single-mixer algorithms, thereby demonstrating the benefit of exploitation and the importance of dynamic exploration-exploitation balance in improving searching efficiency.

翻译：量子近似优化算法的搜索效率依赖于算法的经典和量子两个方面。近期发展了一种包含两个混频器的量子近似贝叶斯优化算法（QABOA），其中采用基于替代模型的贝叶斯优化提升经典优化器的采样效率。利用连续时间量子行走混频器增强探索能力，同时应用广义Grover混频器提升利用能力。本文提出QABOA的扩展以进一步提高其搜索效率。通过两方面增强搜索效率：首先，交替使用两个分别负责探索与利用的混频器；其次，基于基态分布峰度引入新型量子Matérn核函数对量子电路的不确定性进行量化，从而增加获得最优解的概率。将提出的含/不含不确定性量化的新型双混频器QABOA与三个单混频器QABOA在五个离散问题和四个混合整数问题上进行对比。结果表明，在九个测试问题中的五个问题上，所提出的含不确定性量化的双混频器QABOA在效率和一致性方面表现最优。结果还显示，采用广义Grover混频器的QABOA在单混频器算法中性能最佳，这证明了利用能力的价值以及动态探索-利用平衡对提升搜索效率的重要性。