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Quantum computing is an emerging set of technologies which promise to transform aspects of computing in ways that, though increasingly defined, are still largely theoretical. Responsible Innovation (RI) asserts that technologies with potentially transformative capacity on society should be approached with care and forethought; this paper is based on applying RI in one of the UK's National Quantum Technology Hubs. Quantum computing is at a key juncture as it emerges from the laboratory to be of interest commercially. This provides an opportunity to observe and influence the trajectory of this technology. Quantum computing is widely envisioned to have major impacts on computing and society; there are, however, great uncertainties about development timescales and the scope and impact of applications. From experiences with a major quantum computing project in the UK, we discuss the challenges in applying RI to quantum computing. Existing RI practices struggle to address the societal implications of such a complex and innovative technology. We argue that uncovering the visions and sociotechnical imaginaries that inform the development this technology enables RI to make valuable insights into future societal implications of quantum computing. This provides lessons for RI in emerging technologies more widely. [ABSTRACT FROM AUTHOR]