Visualization of the Quantum Fourier Transform Using a Quantum Computer Simulator

The quantum Fourier transform (QFT) is a key subroutine of quantum algorithms for factoring and simulation and is the heart of the hidden-subgroup problem, the solution of which is expected to lead to the development of new quantum algorithms. The QFT acts on the Hilbert space and alters the quantum mechanical phases and probability amplitudes. Unlike its classical counterpart its schematic representation and visualization are very difficult. The aim of this work is to develop a schematic representation and visualization of the QFT by running it on a quantum computer simulator which has been constructed in the framework of this research. Base states, superpositions of base states and entangled states are transformed and the corresponding schematic representations are presented. The visualization of the QFT presented here and the quantum computer simulator developed for this purpose may become a useful tool for introducing the QFT to students and researches without a strong background in quantum mechanics or Fourier analysis.