Measuring the impact of noise on quantum Fourier transforms

Abstract: The field of quantum computing has progressed quickly during recent years, but errors caused by quantum noise still remain as a major issue that prevents accurate computations from being performed on quantum computers. In this study, we measure the impact that these errors have on one of the most fundamental quantum operations, the quantum Fourier transform. The quantum Fourier transform is first repeatedly computed and measured on a simulator, after which noise from two noise models is introduced and the process repeated. The observed output probability distributions are then compared. The results show that the mean absolute error of the noisy results when compared to the ideal results generally decreases as the circuit size increases, while the absolute error increases. The mean arctangent absolute percentage error generally increases as the circuit size increases, up to a certain point where the growth of error stops entirely. The absolute error experienced by individual values generally increases with circuit size and the significance of that value in relation to the other possible values. Finally, input data which produces more values that are more equal in significance are found to be more resistant to error caused by noise, across all metrics of error used. When these results are run through an inverse quantum Fourier transform, however, even small errors will be more significant, and large errors will be less significant, following the same principle as the non-inverse quantum Fourier transform.