The escalating impacts of climate change and the increasing demand for sustainable development and natural resource management necessitate innovative technological solutions. Quantum computing (QC) has emerged as a promising tool with the potential to revolutionize these critical areas. This review explores the application of quantum machine learning and optimization techniques for climate change prediction and enhancing sustainable development. Traditional computational methods often fall short in handling the scale and complexity of climate models and natural resource management. Quantum advancements, however, offer significant improvements in computational efficiency and problem-solving capabilities. By synthesizing the latest research and developments, this paper highlights how QC and quantum machine learning can optimize multi-infrastructure systems towards climate neutrality. The paper also evaluates the performance of current quantum algorithms and hardware in practical applications and presents realistic cases, i.e., waste-to-energy in anaerobic digestion, disaster prevention in flooding prediction, and new material development for carbon capture. The integration of these quantum technologies promises to drive significant advancements in achieving climate resilience and sustainable development.