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In this paper, an adaptive controller is designed for a UAV flight control system against faults and parametric uncertainties based on quantum information technology and the Popov hyperstability theory. First, considering the bounded control input, the state feedback controller is designed to make the system stable. The model of adaptive control is introduced to eliminate the impact by the uncertainties of system parameters via quantum information technology. Then, according to the model reference adaptive principle, an adaptive control law based on the Popov hyperstability theory is designed. This law enable better robustness of the flight control system and tracking control performances. The closed-loop system's stability is guaranteed by the Popov hyperstability theory. The simulation results demonstrate that a better dynamic performance of the UAV flight control system with faults and parametric uncertainties can be maintained with the proposed method.