Experimental study of Shor's factoring algorithm using the IBM Q Experience

We study the results of a compiled version of Shor's factoring algorithm on the ibmqx5 superconducting chip, for the particular case of N=15, 21, and 35. The semiclassical quantum Fourier transform is used to implement the algorithm with only a small number of physical qubits, and the circuits are designed to reduce the number of gates to the minimum. We use the square of the statistical overlap to give a quantitative measure of the similarity between the experimentally obtained distribution of phases and the predicted theoretical distribution of phases for different values of the period. This allows us to assign a period to the experimental data without the use of the continued fraction algorithm. A quantitative estimate of the error in our assignment of the period is then given by the overlap coefficient.