Implementations for Shor's algorithm for the DLP

Abstract

Shor's algorithm for solving the discrete logarithm problem is one of the most celebrated works in quantum computing. It builds upon a quantum circuit performing modular exponentiation. As this is a comparatively expensive process, many approaches for reducing both the number of used qubits and the number of applied gate operations have been proposed. We provide quantum circuits in Qiskit for three different implementation proposals aiming to reduce space complexity and compare their performance regarding their asymptotic gate complexity. We make use of the circuit implementations and Qiskit’s simulation capabilities to compare the actual number of applied gate operations in compiled circuits for small problem instances to aid future applications of this algorithm.