Accordingly a Quora answer
Quantum computation is fully deterministic. A given computation applied to a given starting state will always produce the same final state, every time. What is potentially non-deterministic is extracting the output in classical terms.
So, it looks like it makes sense to introduce probabilistic quantum computation (as opposed to "fully deterministic"). Does it make sense? Does such thing as probabilistic quantum computation exist in physics?
So maybe, for probabilistic quantum computation there is no known proof that there are computable functions of (probabilistic) quantum time complexity strictly above polynomial, is there?