Quantum Fourier transform is said to be similar to Hadamard gate, applying QFT to a set of qubits gives us a new set of amplitudes for each state, which is a linear combination original amplitudes multiplied by e^[(2*piij)/N]
How is this transformation similar to Hadamard's?
What is the use/purpose of linearly combining the state amplitudes?
How can this be used? Could you give me an example, please?