In this paper, we consider a wireless uplink transmission scenario in which an unmanned aerial vehicle (UAV) serves as an aerial base station collecting data from ground users. To optimize the expected sum uplink transmit rate without any prior knowledge of ground users (e.g., locations, channel state information and transmit power), the trajectory planning problem is optimized via the quantum-inspired reinforcement learning (QiRL) approach. Specifically, the QiRL method adopts novel probabilistic action selection policy and new reinforcement strategy, which are inspired by the collapse phenomenon and amplitude amplification in quantum computation theory, respectively. Numerical results demonstrate that the proposed QiRL solution can offer natural balancing between exploration and exploitation via ranking collapse probabilities of possible actions, compared to the traditional reinforcement learning approaches which are highly dependent on tuned exploration parameters.