Pic rel is THE standard textbook on quantum computing. It covers basics of both QM and computation theory in the first chapters to make the topic accessible for both physicists and computer scientists.
Contrary to popular belief you don't need an indepth understanding of QM on the same level as a physicist to get into quantum computing. Since QC only deals with binary observables the more intricate details of infinite dimensional Hilbert spaces or quantum fields are not a prerequisite. For the most part you'll be fine with naive linear algebra in finite dimensions.