I didn't really understand the answer though. The computer is programmable, but the way supremacy is demonstrated is orthogonal to its programmability - it is still demonstrating superiority on just the one problem of simulating itself starting from any initial condition, no?
> 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.
Ah yes, indeed. So it hinges on whether my cat is programmable. Well as it happens my cat has a number N of programmable modes:
1 - cat having its ears tickled
2 - cat watching something move under a sheet that might be a mouse
3 - cat waiting for tin of cat food to be opened
4 - cat wanting to get through a door
etc etc up to 'N'
So a “challenger” generates a random number C between 1 and N, and the challenger then sends C to me and my cat, and I apply the appropriate 'input' to my cat, tickling her ears or openeing a tin of food or whatever, to get her into the correct mode. We then measure her behaviour and then fire up our cluster of computers and run the simulation and then wait for a few months for the numbers to get crunched to verify if the cats behaviour was within expected probability distribution for C.
"Programmable" in this context would mean that you can encode complex computational problems into your cat's behavior. The idea is to distinguish a cat that can only calculate cat behavior (which is of course a very easy problem) from a cat that could eventually be engineered to calculate whatever you want.
If you can solve complex computational problems faster than a cat-sized computer by carefully arranging tins of cat food, it would definitely be fair to say your cat computational supremacy is a significant achievement.
Google's device is not encoding complex computational problems. Its just being told to arrange its qbits into a random series of gates. Could it do the Fizz Buzz algorithm? Or output the Fibonacci sequence? If not, then in what way is it programmable?
It's programmable in the same way an FPGA where you can specify how gates are connected is.
Note that the "random series of gates" is generated on a classical computer, and then the quantum processor is set to that configuration. It's not that you turn on the quantum processor and whatever random uninitialized state is it in.
What's a classical computer, if not silicon arranged into a random series of gates?
I'm not sure how to evaluate the question of whether it could do the Fizz Buzz algorithm. Could it run fizzbuzz.c? No, it doesn't have an OS. Could it perform a sequence of operations isomorphic to "count to 100 by 3s and 5s"? It sounds like Aaronson's answer would be yes, but I think you'll be skeptical (and I am too) about whether that really means anything.
A stone tablet could "perform" a sequence of operations isomorphic to "count to 100 by 3s and 5s". But "count to N by 3s and 5s" for any N : 0 < N < 2^32. Well that'd require a lot of stone.