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The Boolean satisfiability problem (SAT), in particular 3SAT with its boundedclause size, is a well-studied problem since a wide range of decision problemscan be reduced to it. Due to its high complexity, examining potentials ofquantum algorithms for solving 3SAT more efficiently is an important topic.Since 3SAT can be formulated as unstructured search for satisfying variableassignments, the amplitude amplification algorithm can be applied. However, thehigh circuit complexity of amplitude amplification hinders its use on near-termquantum systems. On the other hand, the Quantum Approximate OptimizationAlgorithm (QAOA) is a promising candidate for solving 3SAT for NoisyIntermediate-Scale Quantum devices in the near future due to its simple quantumansatz. However, although QAOA generally exhibits a high approximation ratio,there are 3SAT problem instances where its success probability decreases usingcurrent implementations. To address this problem, in this paper we introduceamplitude amplification-inspired variants of QAOA to improve the successprobability for 3SAT. For this, (i) three amplitude amplification-inspired QAOAvariants are introduced and implemented, (ii) the variants are experimentalcompared with a standard QAOA implementation, and (iii) the impact on thesuccess probability and ansatz complexity is analyzed. The experiment resultsshow that an improvement in the success probability can be achieved with only amoderate increase in circuit complexity.

Amplitude amplification-inspired QAOA: Improving the success probability for solving 3SAT