Author(s)

Zhongwei Wang, Xirui Gou, Ruiqing Fu, Zhixuan Fu

Corresponding Author

Zhongwei Wang

ABSTRACT

Quantum Fourier transform (QFT) plays an eminent role in quantum computation. It creates a superposition of different quantum states, allowing simultaneous calculation, which would take many steps were the same program implemented on a classical computer. The computational speed of a quantum computer is thus boosted dramatically. In this article, we explain the application of QFT in Shor’s algorithm, which was proposed by Peter Shor to factor large integers on quantum computers. Specifically, the principle and design of quantum Fourier transform are explained. We stress the subtle distinction between QFT and its inverse. Since former articles did not emphasize it, we hope it could be a supplement to former articles. Our next work is to verify the existing articles on executing Shor’s algorithm by conducting two experiments on IBMQ of factoring N = 15 in two ways (a = 7 and a = 11). We find that the effect of quantum entanglement might be crucial to the speed boost of factoring large integers in Shor’s algorithm.

KEYWORDS

Quantum; Fourier Transform; Shor’s Algorithm