# An Experimental Study of Shor's Factoring Algorithm on IBM Q

## TL;DR

This paper reports an experimental implementation of Shor's factoring algorithm on IBM's superconducting quantum chip for small numbers, using optimized circuits and a novel method to determine the period without continued fractions.

## Contribution

It demonstrates a practical realization of Shor's algorithm on current quantum hardware with reduced qubit count and gate complexity, and introduces a new approach to period estimation.

## Key findings

- Successful factorization of small numbers on IBM Q hardware
- Use of semi-classical Fourier transform to minimize qubits and gates
- Quantitative error estimation via statistical overlap

## Abstract

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.