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Yep. That's why a quantum computer can break the RSA code so much more easily than classical machines.

Apples and oranges though. I do not know of anyone that has shown non-axiomatic computation on quantum computers is generally more efficient than using classical computers. Everything done with quantum computers to date is classic axiomatic computation, albeit in a different fashion. Without thinking about it too hard, there are aspects of non-axiomatic computation that are probably not amenable to quantum shortcuts.

Non-axiomatic computers have an intrinsic massive parallelism, but it is a very different kind of parallelism than quantum computing exploits.

You clearly have a deeper knowledge of quantum physics than I do, so I'm finding it a bit hard to keep up.

All your points are well taken. Especially the not being able to prove non-determinism from inside a system. Imagine if you found a devices that you thought produced truly random numbers and didn't repeat a sequence. How would you ever know? Even if you let it run for years and it never repeated a sequence, you can't know that the next number it generated wouldn't be the restart of the sequence.

Still, that leaves wetware AI, and I think that has even worse moral implications than AI on silicon. If you have a computer that is self-aware, has free will, but has an organic, living brain instead of a CPU, memory, and hard drive, it's going to be hard to argue that it isn't entitled to some rights. I can see political hysteria of the worst kind surrounding such a situation pretty easily.