John von Neumann is regarded by many as the smartest man of the XX century. Two of his areas of expertise were the foundations of quantum mechanics, and computability theory. He wrote the first QM textbook that clearly explain how observations yield collapse of the wave function, 1932. He was one of the first in the mainstream mathematical community to recognize the significance of Goedel's work on the computability of proofs.
The Church–Turing thesis of the 1930s was the physically computable functions were those defined by Goedel, Church, and Turing.
Not until around 1985 did anyone argue that von Neumann's QM is in direct contradiction to the Church-Turing thesis, and that quantum computers will be able to create computable functions that are beyond what can be done with Turing machines.
How was von Neumann so stupid as to not notice this?
Von Neumann did a lot of work to build early computers, and yet he never commented that with quantum mechanics, he could outdo a Turing machine. Why?
And why didn't anyone else notice it either?
I say that the answer is that there is no such contradiction. The foundations of quantum mechanics do not imply a violation of Church's thesis. It is a myth.
QM says that if you have a system with a |0> state and a |1> state, and if you cannot predict which will be the result of a future measurement, then the formalism represents it as a cat-state, where either is possible. It is like the Schroedinger cat that might be alive or dead, until you open the box and look.
The theory works great, and I don't question it.
But the quantum computing enthusiasts claim that you can some use your uncertainty to do a super-Turing computation. This is like putting a cat in a box, generating some uncertainty about whether the cat is alive, and they trying to use that uncertainty to do a super-Turing computation. At the end, you might open the box to find that the cat was alive all along, but the intervening uncertainty somehow magicly does some super-natural computation.
I don't believe it. The conventional wisdom should be in the validity of Church's thesis, unless someone convincing demonstrates otherwise.