You could say quantum computers do something better than classical computers, but you cannot say they can do something useful better than classical computers. At present, “Quantum supremacy” only applies to toy problems.
Your other question is not so easily answered.
The answer is yes. Sometimes this is referred to as 'quantum supremacy' and some researchers at Google declared it in 2019.
https://www.nature.com/articles/s41586-019-1666-5 https://ai.googleblog.com/2019/10/quantum-supremacy-using-pr...
> One of the most celebrated results in quantum computing is the development of a quantum algorithm for factorization that works in time polynomial in n. This algorithm, due to Peter Shor and known as Shor’s algorithm, runs in O (n3 log n) time and uses O (n2 log n log log n) gates. The first experimental implementation of this algorithm on a quantum computer was reported in 2001, when the number 15 was factored. The largest integer factored by Shor’s algorithm so far is 21.
The only thing it can do faster is to run itself.
It's as if I called a Boeing airliner an aerodynamic computer and each flight a computaion.
In any test flight there are plenty of parameters set for the flight. Are aerodynamic computers programmable?
But in any case, the mere existence of "quantum supremacy" research is a clear indication these are pointless contraptions.
The second half of the article I shared covers the parametrization question you raised.
A successful technology does not need to show theoretical supremacy. Its proponents can simply show the useful services and products it makes.
> Proof of concepts that can not solve "useful" problems seem like an incredibly important milestones to me?
Sure, just don't claim supremacy until you can back it up with an actually reasonable definition of computation.
> Or is your frustration that they are occasionally presented by overly enthusiastic engineers as more than "useless" technology demonstrators (with this frustration I would agree).
It is hard to find any news about quantum computing that is not way over exaggerated.
> The second half of the article I shared covers the parametrization question you raised.
His argument may apply to the teapot example, but for, say, a test flight to fine tune the auto pilot behavior, there are plenty of inputs that can be set. I'd argue the aerodynamic computer supremacy example still stands.
In your first paragraph, while I am sympathetic with your annoyance (pardon my imprecise choice of words), I disagree there too. Mostly because I can imagine the same argument used against Babbage, Lovelace, and Turing, who did their theory (and failed experiment) work decades to a century before a scalable classical computer existed.
But you'll never know, until you look at me.