Earlier quoted context omitted.
Turing machines aren't quantum mechanical, and computation is based on logic. This discussion is philosophical, so I guess it's philosophy all the way down.
Quantum computers don't provide access to novel problems, they provide access to novel solutions. You can use a classic transistor turing machine to solve quantum problems, it's just gonna take way longer.
As such, it doesn't look like reality can be fully simulated by a Turing machine.