  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. Due to its high complexity, examining potentials of
quantum algorithms for solving 3SAT more efficiently is an important topic.
Since 3SAT can be formulated as unstructured search for satisfying variable
assignments, the amplitude amplification algorithm can be applied. However, the
high circuit complexity of amplitude amplification hinders its use on near-term
quantum systems. On the other hand, 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 its success probability decreases using
current implementations. To address this problem, in this paper we introduce
amplitude amplification-inspired variants of QAOA to improve the success
probability for 3SAT. For this, (i) three amplitude amplification-inspired QAOA
variants are introduced and implemented, (ii) the variants are experimental
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.
