Quantum Computing Discrete Logarithms with the Help of a Preprocessed State

Abstract

An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial ingredient of the algorithm is a quantum state that needs to be constructed before we can perform the computation. After one copy of this state is created, the algorithm can be executed arbitrarily many times.