Regev's reduction as a candidate quantum algorithm for the discrete logarithm problem in finite abelian groups
The paper explores using Regev's reduction to turn decoding problems into quantum solvers for discrete logarithms in finite abelian groups. It investigates whether this method can efficiently solve DLOG, particularly for Cheng–Wan instances, finding that while a specific quantum measurement solves every instance unconditionally, its implementation requires exponential resources.