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Nisan comments on Who thinks quantum computing will be necessary for AI? - Less Wrong
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Skimming the article you linked, it looks like Penrose believes human mathematical intuition comes from quantum-gravitational effects. So on Penrose's view it might be possible that AGI requires a quantum-gravitational hypercomputer, not just a quantum computer.
Note that according to Scott Aaronson (in his recent book), Penrose thinks that human minds can solve the Halting problem and conjectures that humans can even solve the Halting problem for machines with access to a Halting oracle.