PostBQP
The addition of postselection seems to make quantum Turing machines much more powerful: Scott Aaronson proved PostBQP is equal to PP , a class which is believed to be relatively powerful , whereas BQP is not known even to contain the seemingly smaller class NP . Using similar techniques , Aaronson also proved that small changes to the laws of quantum computing would have significant effects . 
<triplet> PostBQP <subj> PP <obj> said to be the same as <triplet> PP <subj> PostBQP <obj> said to be the same as