Mathematical Analysis and Simulation of Shor's Algorithm and the Quantum Fourier Transform

In 1994, Peter Shor presented an algorithm for integer factorization that used exponentiallyless operations than the most efficient known algorithm. His algorithm requiresthe use of a quantum computer, a theoretical computational device using quantum mechanicaleffects not utilized in contemporary computers. In this paper we have analysedthe mathematics behind Shor’s algorithm and the quantum circuits on which it operates.We have also studied the Quantum Fourier Transform, a central component of Shor’sAlgorithm. Furthermore we have written a program in C++ to simulate a quantum circuitperforming Shor’s algorithm and the quantum Fourier transform. We were able tounderstand the critical parts of Shor’s algorithm that contribute with the great increasein efficiency compared to classical algorithms.