You have to take into account that quantum processes are governed by a kind of "randomness" that is different from the one in stochastic processes. Scott Aaronson explains the basics of quantum mechanics very succinctly in one of his lectures [1].
The exponential->polynomial speedup we might get from a quantum computer doesn't really apply to stochastic processes, because we can already execute them in polynomial time on a classical computer (just use a random number generator).
Having a quantum computer would still be truly amazing, though. Even just being able to simulate quantum mechanics efficiently would be revolutionary.