The accelerating complexity of Earth system modelling demands computational breakthroughs beyond traditional high-performance computing (HPC). This chapter introduces Climate Modelling 2.0, a next-generation framework integrating quantum computing with HPC to enhance the accuracy, speed and energy efficiency of climate simulations. After reviewing current HPC-based modelling limitations, the chapter explores how quantum algorithms—such as the Quantum Approximate Optimization Algorithm (QAOA) and Quantum Neural Networks (QNNs)—can improve model calibration and sub-grid physics emulation. Two proof-of-concept case studies are presented, demonstrating faster convergence and reduced parameterization bias compared to classical methods. Additional emerging directions are discussed, including quantum-enhanced data assimilation, uncertainty quantification and digital twin frameworks. The findings suggest that quantum–HPC synergy could deliver measurable gains in both computational performance and physical realism. Although full-scale quantum integration remains constrained by hardware maturity, the hybrid approach presented here offers a practical pathway towards sustainable, high-fidelity climate modelling.