Quantum Computing is a computational paradigm that takes into account the laws of Quantum Physics in the steps of the computation which advantages were verified both in Computation and Communications. No scalable quantum computer was developed so far and to execute, to test, and to create new quantum algorithms the simulation of quantum computers on classical computers plays an important role. In this work, we show the design, tools and results obtained for the simulation of the Quantum Fourier Transform algorithm. As a result, we developed an open-source tool, called FTSimulator, and we could simulate up to 12 qubits according to the procedures specified by an experimental test.