Abstract: Anaerobic digestion is a promising technology in the production of renewable energy, in which biogas is the biological energy generated by anaerobic digestion of organic waste. It is necessary to predict and control biogas yield from anaerobic digestion. A multi-quantum filter quantum convolutional neural network with short-term memory is designed. The designed network utilizes the parameterized variational quantum circuit to accept the data 'time window' so as to simulate the short-term memory, and discards too much circuit iteration and parameter number of the multi-quantum filter to make the filter more expressive. In the quantum circuit framework, the optimal convolution and pooling layer circuits are designed to better extract the hidden states in the feature factors. At the same time, the waste management data are strictly preprocessed, and the trend and seasonality in the characteristics are removed by exponential smoothing. The accuracy of the proposed algorithm reaches 83.30%, which is 8% higher than that of the convolutional neural network model (CNN). The root mean square error (RMSE) and mean absolute error (MAE) values are also better than those of artificial neural network (ANN), K-nearest neighbor (KNN) and CNN classical models.