Just read David Deutsch's 1985 paper on the Physical Church-Turing Principle carefully.

https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1985.0070

I think I'm getting the following gist from the work (even though I can't understand the quantum theory in the paper in detail) ...

Maybe someone can correct me if I'm wrong?

There are two argumentative tricks in the paper.

The first is to use a *very* broad definition of a "computing machine" as a generic input-output dynamical system, before restricting the definition to the more customary Turing machine.

The other is hidden in the peculiar assumptions that go into the claim that all finite physical systems are simulable by a universal quantum computer.

Basically, this claim only works if you can formalize the whole universe into some sort of state space (that can then be approximately subdivided into finite subsystems that can be simulated).

Also: simulation only works "with arbitrary precision" but that is not the same as "perfect simulation" as Deutsch defines the term. In practice, the difference is obviously unimportant, but if you want to make the claim that physics *is* (quantum) computation then you have to do better than that.

Finally, I love how he wiggles around the topic of falsifiability, indirectly admitting that the whole idea is of a rather metaphysical rather than physical nature.

What can I say? I'm not sold on this. Not at all.

What I get out of this paper is this: universal quantum computing is a damn good way of simulating physical processes (if it will ever be implemented in a tractable physical system).

Interesting stuff. But no convincing evidence that physics actually *is* computation.

Also interesting: Deutsch suggests Q-logic depth is non-decreasing, just like entropy, in this 1985 paper.

This strongly presages the arguments made in the assembly theory paper I recently discussed in this blog: http://johannesjaeger.eu/blog/assembly-theory-is-cool.

Really not so novel after all, that one...

But what all these papers reveal: there are huge philosophical problems with (pan)computationalism.

It is founded on dodgy equivalences & very peculiar interpretations of the relation between physics & computation.

I'll have much more to say about that soon...