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 the 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 QABOAs with and without uncertainty quantification are compared with three single-mixer QABOAs on two 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 six 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取决于算法中经典部分与量子部分两方面的性能。近期，一种包含两个混频器的量子近似贝叶斯优化算法（QABOA）被提出，其中基于代理模型的贝叶斯优化用于提升经典优化器的采样效率。该算法采用连续时间量子行走混频器增强探索能力，并应用广义格罗弗混频器强化开发能力。本文提出一种QABOA的扩展算法，旨在进一步改善其搜索效率。该改进通过两方面实现：首先，交替使用分别负责探索与开发的两个混频器；其次，基于基态分布峰度构建新的量子马特恩核函数，对量子电路中的不确定性进行量化，从而提升获得最优解的概率。将所提出的含与不含不确定性量化的双混频器QABOA算法与三种单混频器QABOA算法在两类离散问题和四个混合整数问题上进行比较。结果表明，含不确定性量化的双混频器QABOA在六个问题中的五个上展现出最佳的性能效率与稳定性。同时，采用广义格罗弗混频器的QABOA在单混频器算法中表现最优，证实了开发机制的价值以及动态探索-开发平衡对提升搜索效率的重要性。