Solving Large-Scale QUBO with Transferred Parameters from Multilevel QAOA of low depth

The Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum approach for tackling combinatorial optimization problems. However, hardware constraints such as limited scaling and susceptibility to noise pose significant challenges when applying QAOA to large instances. To overcome these limitations, scalable hybrid multilevel strategies have been proposed. In this work, we propose a fast hybrid multilevel algorithm with QAOA parameterization throughout the multilevel hierarchy and its reinforcement with genetic algorithms, which results in a high-quality, low-depth QAOA solver. Notably, we propose parameter transfer from the coarsest level to the finer level, showing that the relaxation-based coarsening preserves the problem structural information needed for QAOA parametrization. Our strategy improves the coarsening phase and leverages both Quantum Relax \& Round and genetic algorithms to incorporate $p=1$ QAOA samples effectively. The results highlight the practical potential of multilevel QAOA as a scalable method for combinatorial optimization on near-term quantum devices.