Solution
= Solution
Writing $\omega_N=e^{2\pi i/N}$, the <quantum Fourier transform> acts on a computational-basis state as
$$
\boxed{
\operatorname{QFT}_N|x\rangle
=\frac1{\sqrt N}\sum_{y=0}^{N-1}\omega_N^{xy}|y\rangle.
}
$$
= Solution
Writing $\omega_N=e^{2\pi i/N}$, the <quantum Fourier transform> acts on a computational-basis state as
$$
\boxed{
\operatorname{QFT}_N|x\rangle
=\frac1{\sqrt N}\sum_{y=0}^{N-1}\omega_N^{xy}|y\rangle.
}
$$