The distributed frequency control system of microgrids, which relies on classical communication networks between distributed generations (DGs) for frequency regulation and restoration, is vulnerable to cyber-attacks. Quantum distributed controllers offer a secure quantum communication scheme but are less efficient because of continuous communication in quantum systems. This paper proposes a quantum distributed event-triggered secondary frequency control strategy for the islanded AC microgrid. The suggested event-triggered control significantly lessens the communication load and is Zeno-free. Furthermore, a novel false data injection attack (FDIA) scenario is introduced for the quantum-microgrid system. The non-periodic nature of communication can be exploited to directly identify and isolate compromised communication links, thereby enhancing the resilience of the quantum-microgrid system. Finally, simulation results on an AC microgrid with four DGs validate the effectiveness of the suggested control scheme.