Problem
Research questions and friction points this paper is trying to address.
discrete logarithm problem
quantum computing
hardware limitations
quantum register size
distributed quantum algorithm
Distributed Quantum Discrete Logarithm Algorithm
🤖 AI Summary
Current quantum hardware struggles to tackle large-scale discrete logarithm problems (DLP). This work proposes a distributed quantum algorithm that operates without quantum communication by partitioning the solution space into subsets and locating the solution through set-intersection detection combined with an optimized quantum phase estimation procedure. The approach achieves, for the first time, a distributed quantum solution to the DLP, significantly reducing the required size of quantum registers on individual nodes while enhancing the overall success probability. Compared to Shor’s algorithm, the proposed method substantially lowers quantum resource demands, offering a practical pathway toward quantum cryptanalysis on near-term, resource-constrained hardware.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
distributed quantum algorithm
discrete logarithm problem
quantum register reduction
set intersection
no quantum communication
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