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Convolutional neural network (CNN) has proven effective at solving difficult image classification problems, but it can be challenging to design its architecture. We try to simplify the search process of the optimal architecture and minimize human participation, so quantum behaved Particle Swarm Optimization with binary encoding (BQPSO) is employed after analyzing the limitations of traditional Particle Swarm Optimization (PSO). To do this, we propose a novel and robust binary encoding strategy which does not require users with domain knowledge on CNN. Then a new quantum behaved evolving strategy is proposed to ensure the effectiveness of evolved CNN architectures. Finally, the performance of our algorithm is measured by the classification accuracy for several benchmark datasets commonly used in deep learning. The experimental results prove that our proposed method can achieve better performance and robustness than the traditional method. This is the first completely automatic algorithm in the area of using quantum behaved PSO to evolve CNN architectures. [ABSTRACT FROM AUTHOR]