quantum gate directory

$$ R_{xx}(\theta) = \exp\left(-i\frac{\theta}{2}X\otimes X\right) = \begin{bmatrix} \cos\frac{\theta}{2} & 0 & 0 & -i\sin\frac{\theta}{2} \\ 0 & \cos\frac{\theta}{2} & -i\sin{\frac{\theta}{2}} & 0 \\ 0 & -i\sin{\frac{\theta}{2}} & \cos{\frac{\theta}{2}} & 0 \\ -i\sin{\frac{\theta}{2}} & 0 & 0 & \cos{\frac{\theta}{2}} \end{bmatrix} $$