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A novel quantum-inspired reinforcement learning (QiRL) algorithm is proposed for navigation control of autonomous mobile robots. The QiRL algorithm adopts a probabilistic action selection policy and a new reinforcement strategy, which are inspired, respectively, by the collapse phenomenon in quantum measurement and amplitude amplification in quantum computation. Several simulated experiments of Markovian state transition demonstrate that QiRL is more robust to learning rates and initial states than traditional reinforcement learning. The QiRL approach is then applied to navigation control of a real mobile robot, and the simulated and experimental results show the effectiveness of the proposed approach.