Circuit implementation of Shor's algorithm for the factorization of small integers in Qiskit

To factor an integer N into a product of two other numbers N₁ and N₂, Shor’s algorithm uses the Quantum Fourier Transform on n qubits, denoted QFT_n, to determine the period r of a Modular Exponentiation Function (MEF), which is later used to compute a factor of N. In this work, we present Shor’s algorithm for factoring an integer of n qubits and illustrate an example with n=4. We implement our algorithm using Qiskit and IBM quantum computers, which also can be adapted on other quantum computing platforms with minor adjustments. We discuss the IBM quantum computer limitations for running our circuit and show the impact of device imperfections on the factored result.