If gravity plays a role in wave function collapse that will pose serious questions for the Church-Turing hypothesis. It might very well make it impossible for

If gravity plays a role in wave function collapse that will pose serious questions for the Church-Turing hypothesis. It might very well make it impossible for non-Quantum computers to accurately model quantum gravity. Penrose does not argue for "something computationally more powerful than objective collapse" rather, he argues that the physical Church-Turing thesis is false due to quantum gravity. Something he is an expert on, btw.