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Has anyone tried any quantum computing programming code that shows or demonstrates the advantage of a quantum computer over classical computers? Thanks a lot.

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    $\begingroup$ That depends on what you mean by "practical". Finding commercial applications for quantum computers is an open problem. $\endgroup$ – Victory Omole Jan 24 at 5:18
  • $\begingroup$ @VictoryOmole Thank you for comment, but how about non-commercially-applied quantum computing programming code that shows or demonstrates the advantage of a quantum computer over classical computers? Thanks a lot. $\endgroup$ – Jennifer S. Jan 24 at 7:27
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There are nothing practical that current quantum computers can do that has advantage over classical computers. But these machines do provide potential speed-up over certain problems like factoring through Shor's algorithm. The biggest number being successful factored through Shor's algorithm is 21. This can be seen in this paper: "Experimental study of Shor’s factoring algorithm using the IBM Q Experience". They tried to factor 35 on that paper there but it wasn't successful. You might have seen larger numbers claimed to be factored by a quantum computer but these methods does not use shor's factoring algorithm, which means you don't have the exponential speed-up that you would get. For instance, factoring a number through the Variational Quantum Factoring algorithm would not give you the speed-up that you want... just because you use a quantum computer, it doesn't mean your computation will be faster. These large number claimed to be factored on a quantum computer sometime are chosen because they fit certain category... so it is easier and the result looks more cooler. Craig Gidney did something pretty funny that you can read about it here: Factoring the largest number ever with a quantum computer. :)

Now, there is recent paper by Craig Gidney (serious this time) presented a hypothetical estimation of the time it would take to factor 2048-bit RSA integers using 20 millions qubits. You can read about it here: "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits". This gives you an idea of the speed-up you would get if you have a quantum computer that meets those specifications.

Again, there are nothing practical that current quantum computers can do that has advantage over classical computers.

If quantum chemistry is what you are interested in, then I would point you to this paper: How will quantum computers provide an industrially relevant computationaladvantage in quantum chemistry? (It might not presented the most fair comparison but it does show that we are still have quite a long way from achieving quantum advantage in this area as well given what we have currently...)

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Any implementation of an algorithm showing theoretical advantage is the case you are looking for (e.g. Shor algorithm has exponential speed-up in comparison with classical algorithms). However, in NISQ era there is a problem with noise which can hinder a performance of the algorithm and in the end you are not able to show the advantage.

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  • $\begingroup$ Thank you for your answer. But since you said "Shor algorithm has exponential speed-up in comparison with classical algorithms', then which integer have you tried the Shor algorithm on a quantum computer to factor but can't be factored by classic computers or the factoring of which on classic computers is slower? and what quantum computing programming code did you try to factor the integer? Thanks a lot. $\endgroup$ – Jennifer S. Jan 24 at 7:47
  • $\begingroup$ @JenniferS.: Actually, as I have a limited access to IBM Q (the free account), I was able to factor only no. 35. I think that currently we are not able to do much more, see here: quantumcomputing.stackexchange.com/questions/14340/… $\endgroup$ – Martin Vesely Jan 25 at 10:45

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