If you drop a glass cup on the ground, it will break and shatter into pieces. This happens all the time and is consistent with quantum mechanics. But it never happens that a shattered glass cup rearranges itself from the ground into someone's hand as a whole glass cup, even though this is also consistent with quantum mechanics. We see from this example that not everything that is consistent with quantum mechanics is possible.
As far as I know, scalable quantum computing has never been demonstrated either backwards in time or forwards in time. So a fortiori, I would think that this would be good enough evidence to suggest that scalable quantum computing is impossible. Yet, some physicists believe that scalable quantum computing is still possible. Why?
Answer
The reason is Shor error correction. Shor demonstrated that by using 9 bits for every bit, you can reverse any decoherence event on any of the 9 bits by doing some measurements on auxiliary quantities. Before the existence of error correction, it was plausible to say (and Unruh did say) the quantum computers are unphysical, because they require no error in a macroscopic system. This is an impossible position to hold past 1996.
The error correction method has been made more efficient since, by Shor and collaborators, and the upshot is that if you make a small quantum computer which is coherent for long enough time, and you can encode some dozens of qubits robustly so that you can reverse the errors faster than they occur, you can scale up the computation indefinitely without problems.
This makes quantum computation feasable for sure, and there is no way to argue that it is impossible without arguing that quantum mechanics fails.
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