# Quantum Fourier Transform circuit

1. Apr 11, 2015

### jimmycricket

I'm having a very hard time understanding how the QFT can be realised using just the Hadamard and controlled rotation gates. Furthermore, I cannot see why swap gates are used to reverse the order of the qubits. I'm embarrassed that dont have much by way of any attempt to show here since I am so stumped by this but I can set up a scenario. Say we wish to perform the transformation on a 3 qubit system in the superposition state (omitting normalization factors)
$\sum\limits_{x=0}^7|{x}\rangle= |{000}\rangle+|{001}\rangle+|{010}\rangle+...+|{111\rangle}=|{1}\rangle+|{2}\rangle+...+|{7}\rangle$

2. Apr 16, 2015