Quantum technologies are emerging as strategic assets with the potential to confer significant economic, technological, and security advantages to governments and corporations that achieve early leadership. As quantum innovations become strategically vital, export controls on these technologies introduce complex legal and policy dilemmas, including tensions between innovation, collaboration, and national security. Quantum computing, in particular, presents unique regulatory challenges due to its layered technological stack and dual-use potential. This chapter offers an in-depth analysis of recent export control measures on quantum computing adopted by the United States and selected European Union Member States. It maps the scope and structure of these controls, examines how they target specific elements of the quantum supply chain, and highlights the shift toward plurilateral regulatory approaches outside traditional multilateral frameworks. Furthermore, it identifies key governance challenges—such as regulating intangible assets, avoiding fragmentation, and adapting to novel quantum paradigms—and provides a forward-looking framework for regulators to design more coordinated and adaptive export control strategies. In addition to analyzing constraints, the chapter identifies a range of quantum-specific enforcement opportunities that are uniquely tied to the physical, architectural, and access-layer characteristics of the technology. These include the physical footprint and centralization of large-scale infrastructure, the potential of cloud-based access models for dynamic and differentiated control, and the modular nature of hardware that allows for granular, component-level restrictions. Rather than offering a normative assessment, the chapter distills emerging patterns and strategic considerations likely to shape the future of quantum technology governance. It assesses that there are certain opportunities and challenges of export controls with regard to quantum computers that may inform regulators’ strategies in this space and help guide the design of adaptive, forward-compatible regulatory approaches.