[jessriedel]

> it is still demonstrating superiority on just the one problem of simulating itself starting from any initial condition, no?

It's the "any initial condition" part that is hard. You cannot put a cat, or even a small molecule, in any one of it's possible initial states, let it evolve, measure the outcome, and get reliable answers. (If you could, that would make it a computer! That's all a computer does, assuming the initial states and evolution are rich enough to, e.g., be Turing complete.)

> The computer is programmable, but the way supremacy is demonstrated is orthogonal to its programmability

The fact that the problem posed by the challenger C is "run an arbitrary quantum circuit" is in fact directly connected to the programmability.