Quantum neural network with parallel training (called PS-QNN) is presented in this study to optimize wireless resource allocation. Instead of sending the whole dataset, each edge only requires to send the statistical parameters of the dataset; hence reducing the dimension of training data. As a particular case, the proposed PS-QNN is utilized to optimize transmit precoding and power allocation in non-orthogonal multiple access with multiple-input and multiple-output antennas (MIMO-NOMA). Compared to the conventional training method, analysis shows that the proposed parallel training yields a lower complexity, while achieving a comparable sum rate compared to conventional method.