On the success probability of quantum order finding. (arXiv:2201.07791v1 [quant-ph])

We prove a lower bound on the probability of Shor's order-finding algorithm
successfully recovering the order $r$ in a single run. The bound implies that
by performing two limited searches in the classical post-processing part of the
algorithm, a high success probability can be guaranteed, for any $r$, without
re-running the quantum part or increasing the exponent length compared to Shor.
Asymptotically, in the limit as $r$ tends to infinity, the probability of
successfully recovering $r$ in a single run …

order quantum