# What is the difference between classical and quantum computers as well as computing (permuting) itself?

Theoretically and for sure physically (I know the quantum physics behind it) I know something about it. But not that much. That's why I ask the question here. I'm very interested. The only answer to it made it already much clearer, though not into detail, of course.

Recently, as anyone of you knows, G**gle succeeded in quantum supremacy. Which is to say they built a quantum computer (QC) that did the given job about one and a half billion ($$2^{73}?$$) times as fast as a classical computer (CC).

While being zillions [or more;)] times faster in executing programs [or algorithms(?)], I think, for example, the conditions under which you can use a QC are different than those of a CC, which is why I ask this question. You (maybe very very far away in the future, if Nature still exists then) can't make them very small and portable, for example.

Are the programs and programming, in other words, the jobs to be ordered, be different? I assume yes because of the fact that the QC is superfast in making (instead of calculating) zillions (or even still more) different permutations of whatever kind of objects (like a randomly made permutations of bits, like in the Ggle experiment case). I've heard QC's can be used in meteorology, but (as a side question) in what way is there a question of permutations? More generally, for what kind of jobs are QC's designed or programmed to make such permutations? Or is my assumption that a QC can **only make permutations wrong?

I would be careful with so-called "quantum supremacy". This term means that there are some tasks where quantum computers are faster than classical ones. However, a speed-up is different for different task, e.g. quantum algorithms allow exponential speed-up of integer factoring (Shor algorithm) or calculating values of $$x^{T}Mx$$, where $$x$$ is a solution of $$Ax=b$$ (HHL algorithm) but speed-up for searching (Grover algorithm) is only quadratic. Moreover, there are some tasks where quantum computers bring no speed-up (e.g. binary function parity evaluation).