  In our thesis, we try to shed more light onto the complexity of quantum
complexity classes by refining the related part of the hierarchy. First, we
review the basic concepts of quantum computing in general. Then, inspired by
BQP, we define new complexity classes. They are placed between BPP and PSPACE.
We show that they incorporate the current important quantum algorithms.
Furthermore, the importance of the unitarity constraint given by quantum
mechanics is revealed. Without this requirement, we naturally arrive at the
class AWPP, which was up to now thought to be just an artificially defined
class. We hope that some of our newly defined classes could find their use in
proving results about BQP.
