The growing constraints of conventional modelling frameworks in predicting non-linear, multi-scale interactions in Earth systems due to time-dependent policy restrictions are on the rise particularly as the climate crisis is intensifying. In this chapter, the authors discuss how quantum computing and artificial intelligence can be combined to solve these modelling problems. The Q-AI ClimateNet is a new architecture proposed that is a combination of convolutional neural networks and parameterized quantum circuits to improve spatiotemporal climate predictions. Q-AI ClimateNet trained on a hybrid dataset of CMIP6 projections, ERA5 reanalysis and NOAA observations is better at both accuracy and efficiency than classical CNN-LSTM baselines. It is able to capture spatial gradients, minimize RMSE and increase R2 scores using less energy and less inference time. The model shows a very good performance in high latitude areas where it is effective at modelling non-linear climate feedbacks such as polar amplification. Another aspect of the chapter is the constrictions of the modern quantum hardware, the future research prospects, and more generally what the integration of Q-AI can bring to scalable and sustainable climate modelling.