The Boolean satisfiability problem (SAT), in particular 3SAT with its bounded clause size, is a well-studied problem since a wide range of decision problems can be reduced to it. The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for solving 3SAT for Noisy Intermediate-Scale Quantum devices in the near future due to its simple quantum ansatz. However, although QAOA generally exhibits a high approximation ratio, there are 3SAT problem instances where the algorithm’s success probability when obtaining a satisfying variable assignment from the approximated solution drops sharply compared to the approximation ratio. To address this problem, in this paper, we present variants of the algorithm that are inspired by the amplitude amplification algorithm to improve the success probability for 3SAT. For this, (i) three amplitude amplification-inspired QAOA variants are introduced and implemented, (ii) the variants are experimentally compared with a standard QAOA implementation, and (iii) the impact on the success probability and ansatz complexity is analyzed. The experiment results show that an improvement in the success probability can be achieved with only a moderate increase in circuit complexity.

中文翻译：

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幅值放大启发的 QAOA：提高解决 3SAT 问题的成功概率

布尔可满足性问题 (SAT)，特别是具有有限子句大小的 3SAT，是一个经过充分研究的问题，因为可以将各种决策问题简化为它。量子近似优化算法 (QAOA) 由于其简单的量子模拟，是在不久的将来解决嘈杂中尺度量子设备 3SAT 问题的有前途的候选算法。然而，尽管 QAOA 通常表现出较高的逼近率，但在 3SAT 问题实例中，算法从逼近解中获得满意的变量分配时的成功概率与逼近率相比急剧下降。为了解决这个问题，在本文中，我们提出了受幅度放大算法启发的算法变体，以提高 3SAT 的成功概率。为此，(i) 引入并实现了三个受幅度放大启发的 QAOA 变体，(ii) 将这些变体与标准 QAOA 实现进行实验比较，(iii) 分析对成功概率和 ansatz 复杂性的影响。实验结果表明，只需适度增加电路复杂度即可实现成功概率的提高。