We have chosen the format of a living review, which implies that it will be frequently updated and is open for community contributions. In this way, the review will continue to remain relevant as the  eld develops. It is worth noting that this living review does not qualify as a review of QC in general. We encourage the reader to look elsewhere in the literature for original research and reviews in areas of pure and applied quantum computing less relevant to plasma physics. This project was heavily inspired by a similar e ort in the area of Machine Learning for High Energy Physics [FN21].