Mermin is perhaps best known as the co-author of 'Solid State Physics', a longstanding text of its subject. But his interests are diverse, and one of these is presented here. He explains the intriguing use of quantum computing. Starting with the concept of a Qbit.
The text assumes you've done some non-relativistic quantum mechanics. After all, the entire subject is based on quantum effects producing different results than traditional computing. You should know the bra and ket notation, that was first introduced by Dirac. This notation is amazingly concise and pervades the text. It is probably fair to say that 90% of the discussion uses this notation.
The derivations are elegant and surprisingly simple, compared to the intricacies of other applications of quantum mechanics. There is relatively little discussion of experimental methods. This is primarily a theoretical text.
One conclusion is that this field is young. No serious computations are yet capable, compared to those on computers using traditional classical physics.