# 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?

Does anyone have some more thoughts about this?

## 1 Answer

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).

Regarding your question on programming. Quantum computers are based on different paradigm than classical ones. Programming of quantum computers can be done via languages like Qiskit or Q#, which are more or less same as classical programming languages like C++. However, underlying circuity of quantum computers are totally different from classical ones.

Regarding question on application in meteorology. Currently I know about none but principialy it could be possible as atmosphere is a stochastic system and quantum computers can simulate those.

• According to what I've read your answer, you seem to know a lot about it. Why does the Grover algorithm (is that the same as a program, but differently said?) speed up the searching quadratically? In other words, why can't the different results from the search, or the search itself, Or maybe even the comparison between them (to find out the best result has been found) speed up? – Deschele Schilder Dec 20 '19 at 5:34
• First question: Algorithm is a "recipe" how to do something, program is composed of algorithms. But probably you can say that program is algorithm itself. Second question: The reason is hiden in mathematical derivation of Grover algorithm complexity and it is not easy to explain in plain words. See for example Wikipedia for a proof of quadratic speed-up: en.wikipedia.org/wiki/Grover%27s_algorithm – Martin Vesely Dec 20 '19 at 6:58
• Thanks for your effort! – Deschele Schilder Dec 20 '19 at 7:25
• Your are welcome If you are satisfied with my answer, could you please accept it? Thanks. – Martin Vesely Dec 20 '19 at 7:49
• There you go!!! – Deschele Schilder Dec 20 '19 at 8:23