Regev recently introduced a quantum factoring algorithm that may be perceived as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factoring algorithm to an algorithm for computing discrete logarithms in a natural way. Furthermore, we discuss natural extensions of Regev's factoring algorithm to order finding, and to factoring completely via order finding. For all of these algorithms, we discuss various practical implementation considerations, including in particular the robustness of the post-processing.

翻译：Regev近期提出了一种量子分解算法，可视为Shor分解算法的$d$维变体。本研究将Regev的分解算法自然地扩展为计算离散对数的算法。此外，我们还讨论了Regev分解算法在序数求解以及通过序数求解实现完全分解方面的自然扩展。针对所有这些算法，我们探讨了实际实现中的各种考量因素，特别关注后处理的鲁棒性。