Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current hardware limitations, the scale of DLP instances that can be addressed by quantum computers remains insufficient. To overcome this limitation, we propose a distributed quantum discrete logarithm algorithm that reduces the required quantum register size for solving DLPs. Specifically, we design a distributed quantum algorithm to determine whether the solution is contained in a given set. Based on this procedure, our method solves DLPs by identifying the intersection of sets containing the solution. Compared with Shor's original algorithm, our approach reduces the register size and can improve the success probability, while requiring no quantum communication.

翻译：用量子计算机解决离散对数问题（DLP）是一项具有重要意义的根本性任务。除肖尔算法外，近年来许多研究者提出了替代方案。然而受当前硬件条件限制，量子计算机可处理的DLP实例规模仍显不足。为突破此局限，我们提出一种分布式量子离散对数算法，该算法可降低求解DLP所需量子寄存器规模。具体而言，我们设计了一种分布式量子算法用于判定解是否存在于给定集合中。基于该过程，本方法通过识别包含解的集合交集来求解DLP。与肖尔原始算法相比，本方法在无需量子通信的前提下，既降低了寄存器规模，又能提升成功概率。