The core idea of quantum computing is that the particle dynamics of our universe are so inefficiently implemented on the substrate universe that we can harvest some of the substrate computations to escape the computational class of mechanical computation.
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My experience is that 'the computational model covers everything' is the default—but this may be due to the company I keep ;) If there were something non-computational, we couldn't model it; could only chart boundaries where computational applicability ends.
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The character of conscious experience hints at something potentially non-computational. Computation is reversible, so if we run a conscious system backwards you should get reversed experience, but that seems, at best, nonsensical. Aaronson sees a link here to thermodynamics.
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I also agree "non-computational process" could never be constructed because it's basically self-contradictory. Poor choice of words on my part.
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