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We have quantum computers that can run the Shor algorithm, we managed to factor the number 21 (=3x7) with it in 2012, I am not aware of any improvement to this day.

D-Wave has been used to factor larger integers, but not using the Shor algorithm as it can't do that, it is not a general purpose quantum computer but a specialized "quantum annealer".

All of these attempts have involved some kind of trickery, and even the largest numbers claimed to have been factored are all ridiculously small compared to what we can do with classical computers. This is why these attempts are not taken very seriously: the preprocessing steps done with classical computers take much more time than what it would take for that classical computer to find the solution.



They used the fact that 21 = 7 x 3 in order to reduce gate-count.

The full-Shor has never been run on a hardware device IIRC.

(quite-funny when you see everyone and their mom hyping QC).




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