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So I was looking at Shor Algorithm for prime factorization and I have some doubts in the arithmetic part.

Let's define a function f that : f(x) = a^{x}mod N. The middle step in shor algorithm is to calculate, simultaneously, all values of f. In some papers and books, I saw some high level implementation of this block, but nothing concrete. Can someone explain to me, how they do this?

In some implementations they use Controlled-Gates. Ok, that's fine, but the control qubit is always in some superposition of states. So what happens in this cases?

Thanks!

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# I Arithmetic Block in Shor Algorithm

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