Solution
= Solution
With $\omega=e^{2\pi i/Q}$, the <quantum Fourier transform> over the additive group $\mathbb Z_Q$ is
$$
\boxed{
\operatorname{QFT}_Q|a\rangle
=\frac1{\sqrt Q}\sum_{b=0}^{Q-1}\omega^{ab}|b\rangle}.
$$
= Solution
With $\omega=e^{2\pi i/Q}$, the <quantum Fourier transform> over the additive group $\mathbb Z_Q$ is
$$
\boxed{
\operatorname{QFT}_Q|a\rangle
=\frac1{\sqrt Q}\sum_{b=0}^{Q-1}\omega^{ab}|b\rangle}.
$$