Who was/were the first person/people to introduce the topic of quantum complexity theory and problem classes like BQP and QMA?
which apparently built on the idea of a "quantum proof" suggested by
An important relative to QMA, which is perhaps more delicate but which in a certain respect is a more exact analogue of NP for quantum computation, is the class QMA1 (Complexity Zoo), in which the completeness constraint is perfect (i.e. for YES instances, there is a "quantum proof" with acceptance probability 1, albeit for a noiseless quantum computer). This was defined in
There are other interesting quantum classes, of course. If you want an introduction to the subject, a good start would be