Phase matching in Grover-QAOA for solving 3-SAT problems

The Quantum Approximate Optimization Algorithm (QAOA) is a promising framework for combinatorial optimization, yet its performance is often hindered by the complexity of parameter optimization. In this work, we investigate phase relationships in Grover-QAOA (G-QAOA) for solving 3-SAT problems and introduce a novel phase matching condition that simplifies the optimization landscape. By aligning the phases of the problem and mixing Hamiltonians, our approach reduces the number of variational parameters from 2p to p, significantly lowering computational overhead. We further propose single-angle G-QAOA, an extension that enables additional parameter reduction. Numerical simulations demonstrate that our method achieves success probabilities comparable to those of standard G-QAOA while requiring fewer quantum circuit evaluations. These results highlight the potential of our proposed G-QAOA for practical implementation on near-term quantum hardware.