Is there any quantum computing which does not rely on decoherence prevention techniques? Coherence is what makes quantum computers work in the first place.
What level of argument would you like? Linearity means that the transition functions that map between timeline amplitude distributions be linear. That is indeed a necessary condition on the transition functions. It looks like you want to exclude all transition functions that are not permutations, ie that don’t preserve the distribrution’s histogram. The functions I use for amplitude amplification here are one which flips the amplitude of the timeline that ran the AI, and Grover’s diffusion operator, which redistributes amplitudes to the flipped one’s benefit. If linearity were a sufficient condition, I wouldn’t need these: I could simply use the function that maps the amplitudes of all timelines that did not run the AI to 0, which is linear.
I agree that the ZF-prover use of an AI box is only useful if we actually find a relevant mathematical statement. In the end, this post has no new insight on how useful AI boxes are, only how safe they can be made. Therefore I should make no claims about usefulness and remove the ZF section.
Is there any quantum computing which does not rely on decoherence prevention techniques? Coherence is what makes quantum computers work in the first place.
What level of argument would you like? Linearity means that the transition functions that map between timeline amplitude distributions be linear. That is indeed a necessary condition on the transition functions. It looks like you want to exclude all transition functions that are not permutations, ie that don’t preserve the distribrution’s histogram. The functions I use for amplitude amplification here are one which flips the amplitude of the timeline that ran the AI, and Grover’s diffusion operator, which redistributes amplitudes to the flipped one’s benefit. If linearity were a sufficient condition, I wouldn’t need these: I could simply use the function that maps the amplitudes of all timelines that did not run the AI to 0, which is linear.
I agree that the ZF-prover use of an AI box is only useful if we actually find a relevant mathematical statement. In the end, this post has no new insight on how useful AI boxes are, only how safe they can be made. Therefore I should make no claims about usefulness and remove the ZF section.