I am completely new to quantum computing and playing QuantAttack. While playing, I found something strange: SZS turns into Z.
According to the Wikipedia article that the game recommends reading, SZS must disappear because:
$$ SZS = \begin{pmatrix}1 & 0 \\\\ 0 & i\end{pmatrix} \begin{pmatrix}1 & 0 \\\\ 0 & -1\end{pmatrix} \begin{pmatrix}1 & 0 \\\\ 0 & i\end{pmatrix} = \begin{pmatrix}1 & 0 \\\\ 0 & 1\end{pmatrix} = I $$$$ SZS = \begin{pmatrix}1 & 0 \\ 0 & i\end{pmatrix} \begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix} \begin{pmatrix}1 & 0 \\ 0 & i\end{pmatrix} = \begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix} = I $$
Is there some weird quantum thing I missed, or is it just a game bug?