quantum gate directory
$zz$ Rotation
Symbol
$R_{zz}$
Description:
Two-qubit rotation generated by $Z \otimes Z$.
Alternate notations:
- $R_{zz}(\theta)$
- $\mathrm{RZZ}(\theta)$
- $ZZ(\theta)$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.RZZGate
|
| PennyLane |
pennylane.IsingZZ
|
| Cirq |
cirq.ZZPowGate
ⓘ
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
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.
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