quantum gate directory
$z$ Rotation
Symbol
$R_z$
Description:
Rotation about the $z$ axis of the Bloch sphere.
Alternate notations:
- $R_z(\theta)$
- $\mathrm{Rz}(\theta)$
- $Z(\theta)$
- $Z_\theta$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.RZGate
|
| PennyLane |
pennylane.RZ
|
| Cirq |
cirq.Rz
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
The $R_z$ gate rotates a qubit by angle $\theta$ around the $z$ axis, adding a relative phase between $|0\rangle$ and $|1\rangle$.
$$ R_z(\theta) = \exp\left(-i\frac{\theta}{2}Z\right) = \begin{bmatrix} \mathrm{e}^{-i\frac{\theta}{2}} & 0 \\ 0 & \mathrm{e}^{i\frac{\theta}{2}} \end{bmatrix} $$
Properties
- Often implemented virtually as a frame update in many platforms.
- Combined with $R_x$ or $R_y$ for universal single-qubit control.
- Equivalent to a phase shift up to a global phase.
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