An Experimental Study of Shor's Factoring Algorithm on IBM Q
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 semi-classical 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 one 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.
Mirko Amico Zain H. Saleem Muir Kumph