Fault recovery and network reconfiguration in distribution systems are critical tasks for ensuring the secure and stable operation of power networks. Traditional optimization approaches are often limited by a trade-off between solution accuracy and computational efficiency when addressing this problem. To overcome these limitations, a hybrid algorithm integrating QAOA (quantum approximate optimization algorithm) with ADMM (alternating direction method of multipliers) was proposed. By combining the advantages of quantum computing and classical optimization techniques, both the efficiency and accuracy of the fault recovery and reconfiguration process were enhanced. QAOA was employed to accelerate the global search for optimal solutions through quantum parallelism, while ADMM was utilized to efficiently handle large-scale constrained optimization. The proposed algorithm were applied to the IEEE 33-bus and 69-bus distribution systems, achieving total cost reductions of 40.39% and 50.82%, respectively, under two test scenarios. Comparative experiments with conventional algorithms demonstrate the superior solution accuracy and global search capability of the proposed method, indicating its effectiveness as a novel solution framework for distribution network fault recovery and reconfiguration problems.