You can't compute the exact result of a quantum measurement. Now, randomness is a somewhat separate concept from computation. But still, a Turing Machine can't

You can't compute the exact result of a quantum measurement. Now, randomness is a somewhat separate concept from computation. But still, a Turing Machine can't predict how a quantum system will behave after a measurement, so in some sense it's not computable. The best you can do is to compute the wavefunction and the resulting probabilities of the various possibilities.