The Quantum Fourier Transform is a linear transformation on quantum bits and is the quantum analog of the discrete Fourier transform. In other words, it performs a change of basis on the target qubits from the standard basis to the so called Fourier basis.

In our example, we prepare the state |01010⟩ than apply the circuit for the QFT transform on five qubits and then apply our built-in QFT-Dagger gate. The final state as expected is |01010⟩, same as the initial state.

In important detail to be noted here is that the ordering of gates in the expaned QFT gate circuit shown here follows the Big-Endian ordering convention, so if you want to analyse the circuit simulation output you should check the BigEndian checkbox on the toolbar. As a side note, our built-in QFT and QFT-† gates have been adapted to work with both the Big and LittleEndian qubit ordering conventions.