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The Quantum Approximate Optimization Algorithm (QAOA) exhibits significantpotential for tackling combinatorial optimization problems. Despite its promisefor near-term quantum devices, a major challenge in applying QAOA lies in thecost of circuit runs associated with parameter optimization. Existing methodsfor parameter setting generally incur at least a superlinear cost concerningthe depth p of QAOA. In this study, we propose a novel adiabatic-passage-basedparameter setting method that remarkably reduces the optimization cost,specifically when applied to the 3-SAT problem, to a sublinear level. Beginningwith an analysis of the random model of the specific problem, this methodapplies a problem-dependent preprocessing on the problem Hamiltoniananalytically, effectively segregating the magnitude of parameters from thescale of the problem. Consequently, a problem-independent initialization isachieved without incurring any optimization cost or pre-computation.Furthermore, the parameter space is adjusted based on the continuity of theoptimal adiabatic passage, resulting in a reduction in the disparity ofparameters between adjacent layers of QAOA. By leveraging this continuity, thecost to find quasi-optimal parameters is significantly reduced to a sublinearlevel.

Adiabatic-Passage-Based Parameter Setting for Quantum Approximate Optimization Algorithm