quantum gate directory

The $R_{zz}$ gate implements an Ising-type interaction with rotation angle $\theta$.

$$ \begin{align*} R_{zz}(\theta) & = \exp\left(-i\frac{\theta}{2}Z\otimes Z\right) \\ & = \begin{bmatrix} \mathrm{e}^{-i\frac{\theta}{2}} & 0 & 0 & 0 \\ 0 & \mathrm{e}^{i\frac{\theta}{2}} & 0 & 0 \\ 0 & 0 & \mathrm{e}^{i\frac{\theta}{2}} & 0 \\ 0 & 0 & 0 & \mathrm{e}^{-i\frac{\theta}{2}} \end{bmatrix} \end{align*} $$

Properties

• Entangling for $\theta$ not a multiple of $\pi$.
• Can be implemented with two CNOTs and a single-qubit $R_z$ rotation.