Quantum technologies (QT) are being awaited with excitement. They are supported by many governments, the corporate sector, international bodies and technology forecasters. There is discursive investment as well in terms of creating expectations and laying down a vision for the ‘Second Quantum Revolution’. Science and technology studies are also playing their part to think of the quantum future along with philosophical discussions around it. These visions and expectations perform an implicit and latent function of steering policy proposals and governance. At the current stage of development of quantum technologies, a comprehensive and cogent legal framework is hard to envisage. As it is difficult to foresee the final shape of these technologies, a way to proceed can be to focus on the legal enquiry related to economic, political and policy factors which contribute to its material emergence. This can broaden the focus from thinking about its impact to contextualizing its production and development. Further, it allows a way of determining the extent to which social science and ethical frames can apply to the governance of QT, given the legal and practical realities of technology production and use. This article maps the myriad governance frameworks being envisaged to think about the future of QT. It zooms onto the discussion related to the access divide being framed for QT to understand the points of legal intervention. It uses the case of quantum computing to understand the way legal and practical policy solutions have been ideated. It highlights the way these solutions entrench power of digital infrastructure providers further. This seeks to motivate further work to expand the scope of a legal framework for QT.