The twenty-first century’s grand challenges in resource sustainability, from smart grid management to global logistics, involve optimization problems of unprecedented scale and complexity that often exceed the limits of classical computational methods. This chapter explores the synergistic integration of quantum machine learning (QML) and High-Performance Computing (HPC) as a transformative pathway to address these challenges. We posit that QML algorithms can act as specialized co-processors within a larger HPC workflow, handling complex sub-tasks where a quantum heuristic advantage is suspected. The core contribution is the proposal and analysis of a novel framework, the Quantum–Classical Hybrid Optimization Network (Q-CHRON). We provide a detailed algorithmic blueprint for Q-CHRON, which utilizes a quantum-actored reinforcement learning architecture for dynamic decision-making. The framework is validated through a simulated case study on smart grid optimization, where it demonstrates a significant reduction in operational cost and faster convergence compared to a classical baseline. The discussion extends to practical implementation considerations, including hardware resource allocation and energy consumption, and explores the framework’s extended applications in water distribution, supply chain logistics, and carbon capture. Finally, we address the economic, ethical, and hardware roadmap challenges, arguing that the strategic fusion of QML and HPC is pivotal for achieving sustainable resource management.