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Given a periodic function $f(x+r) = f(x)$, the period-finding procedure of Shor's algorithm can find the period $r$ using $\mathcal{O}(1)$ oracle calls and $\mathcal{O}(poly(\log N))$ operations where a high probability of success is assured after repeating the procedure $\mathcal{O}(\log \log r)$ times [1]. The number of times the procedure must be repeated ...

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