As the world faces mounting climate challenges, the demand for computational tools capable of solving complex, high-dimensional problems has never been greater. Quantum computing, with its ability to simulate molecular interactions and solve optimization problems beyond the reach of classical systems, offers transformative potential for advancing global sustainability goals. This paper explores the emerging role of quantum computing in addressing key climate and energy challenges, including carbon capture, energy storage, renewable integration, and low-carbon supply chain optimization. Drawing on recent industrial initiatives and quantum research programs, the paper outlines how quantum algorithms—such as the Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE), and Quantum Machine Learning (QML)—are being applied to accelerate material discovery and decision-making in energy systems. It also critically examines the limitations of current quantum hardware, the shortage of interdisciplinary talent, and the need for ethical governance in dual-use scenarios. Policy recommendations are proposed to align quantum research with sustainability outcomes, including mission-oriented funding, open-access infrastructure, sustainability impact assessments, and global commons frameworks. The paper argues that without inclusive access, targeted policy, and ethical foresight, quantum innovation risks deepening technological inequities. Ultimately, this conceptual work emphasizes that quantum computing must not only be a frontier of computation but also a purposeful instrument in the global transition toward net-zero emissions and environmental resilience.