Coding Shor's Algorithm

Qiskit

This is Qiskit's code for Shor’s Algorithm. In this example, we factorize $N=15$ with $k=8$ counting qubits. Remember that we need roughly $2n$ qubits for obtaining a good accuracy, where $n$ is the number of bits needed to represent $N$. Also, notice the implementation of $QFT^\dagger$ that allows us to reconstruct the period $r$ of the function by transferring the phase information into our qubits for measurement. You can find further details at the Qiskit Textbook here. The code below uses exponentially many gates to apply the $UROT$ operations. The polynomial-gates implementation is given in the references section of Qiskit on the link provided earlier.