On the success probability of quantum order finding
Abstract
We prove a lower bound on the probability of Shor's order-finding algorithm successfully recovering the order 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 , without re-running the quantum part or increasing the exponent length compared to Shor. Asymptotically, in the limit as tends to infinity, the probability of successfully recovering in a single run tends to one. Already for moderate , a high success probability exceeding e.g. can be guaranteed. As corollaries, we prove analogous results for the probability of completely factoring any integer in a single run of the order-finding algorithm.
Keywords
Cite
@article{arxiv.2201.07791,
title = {On the success probability of quantum order finding},
author = {Martin Ekerå},
journal= {arXiv preprint arXiv:2201.07791},
year = {2024}
}
Comments
This revision resolves a minor issue in Alg. 4, and addresses a number of other minor issues. It furthermore adds a number of extensions and clarifications, in particular with respect to potential optimizations. No key results or findings in the original version of the manuscript are affected by this revision