  In recent years, quantum computing has emerged as a transformative force in
the field of combinatorial optimization, offering novel approaches to tackling
complex problems that have long challenged classical computational methods.
Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out
for its potential to efficiently solve the Max-Cut problem, a quintessential
example of combinatorial optimization. However, practical application faces
challenges due to current limitations on quantum computational resource. Our
work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a
warm-start technique. This sacrifices affordable computational resource on
classical computer to reduce quantum computational resource overhead, enhancing
QAOA's effectiveness. Experiments with various GNN architectures demonstrate
the adaptability and stability of our framework, highlighting the synergy
between quantum algorithms and machine learning. Our findings show GNN's
potential in improving QAOA performance, opening new avenues for hybrid
quantum-classical approaches in quantum computing and contributing to practical
applications.
