I am not shure that it has been demonstrated that a QM mechanis is necessarily solely of a Turing architecture.
The Bekenstein Bound gives limits both on the expected maximum number of quantum states encodable in a given volume of space and on the expected maximum number os transitions between these states. If this bound holds (and it certainly seems to hold for EM fields), then a probabilistic Turing machine will be able to simulate it.
Also there is the potential to use neural networks at these levels (which are not necessarily reducable to Turing models, the premise has never been proven)
If you have infinite precision, the statement is unproven. If you have finite precision, you get a Turing machine. You never get infinite precision in real life, even with quantum superposition. Steve Smale did some work a few years ago where he made Turing-type machines out of real numbers, i.e. infinite precision. P=NP for this model, and the proof is fairly easy. From an information-theoretic point of view, you can encode two real numbers inside of another one and do computations in that encoded form, because a real number encodes an infinite amount of information. If it's finite, it's a Turing machine. If it's expected finite, it's a probabilistic Turing machine. If it's infinite, it cannot be implemented in hardware. Eric