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Quantum-inspired evolutionary algorithm (QEA) has proved to be an effective method to design neural networks with few connections and high classification performance. When a quantum-inspired evolutionary neural network (QENN) converges in the training phase, subsequent training is fruitless and time-wasting. Therefore, it is important to control the number of generations of QENN. The analysis on the convergence property of quantum bit evolution can contribute to designing a safe termination criterion that can always be reached. This paper proposes an appropriate termination criterion based on the average convergence rate (ACR). Experiments on classification tasks are conducted to demonstrate the effectiveness of our method. The results show that the termination criterion based on ACR can duly stop the training process of QENN and overcome the limitations of the termination criterion based on the probability of generating the best solution (PBS). [ABSTRACT FROM AUTHOR]