The maximum power exchange section is playing an important role in analyzing the interoperation of network microgrids. Mathematically, the problem is formulated into a weighted Max-Cut problem, which is non-deterministic polynomial-time hard (NP-hard). A Quantum Approximate Optimization Algorithm (QAOA) is introduced in this paper to search the approximate maximum power exchange sections in networked microgrids. QAOA is a hybrid quantum-classical algorithm, which uses a classical optimizer to train a parametrized quantum circuit. Layer number and angle parameters of the quantum circuit are discussed, which highly impact the performance of QAOA. Numerical examples on a typical reconfigurable networked microgrid system test and verify the effectiveness of QAOA in getting the maximum power exchange sections. This quantum computing implementation sheds light on the development of quantum algorithms to resolve the challenges in power systems that are hard to solve by classical computers.