You have poster drafts due Friday! I’ll try to make this daily post short, but it would be good if you do a bit of basic computation with the QFT.
Apply the $4 \times 4$ QFT matrix to the state
$\frac{1}{\sqrt{2}} \left(
|00 \rangle +
\frac{1+i}{2} |01 \rangle +
\frac{1-i}{2} |11 \rangle
\right)$
Draw the 8th roots of unity in the complex plane and label them. You can use the $8$-th root of unity notation $\omega := \omega_8 = e^{i \pi/4}$. But simplify it so that the labels are from the set $\{1,-1,i,-i, \omega, -\omega, i\omega, -i\omega\}$.
Write down the QFT matrix of dimension $8 \times 8$. You can use the $8$-th root of unity notation $\omega := \omega_8 = e^{i \pi/4}$. But simplify it so that the entries are all from the set $\{1,-1,i,-i, \omega, -\omega, i\omega, -i\omega\}$.