quantum gate directory
$x$ Rotation
Symbol
$R_x$
Description:
Rotation about the $x$ axis of the Bloch sphere.
Alternate notations:
- $R_x(\theta)$
- $\mathrm{Rx}(\theta)$
- $X(\theta)$
- $X_\theta$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.RXGate
|
| PennyLane |
pennylane.RX
|
| Cirq |
cirq.Rx
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
The $R_x$ gate rotates a qubit by angle $\theta$ around the $x$ axis.
$$ R_x(\theta) = \exp\left(-i\frac{\theta}{2}X\right) = \begin{bmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin{\frac{\theta}{2}} & \cos\frac{\theta}{2} \end{bmatrix} $$
Properties
- $R_x(\pi) = -iX$ (global phase).
- Together with $R_z$ it forms a universal set for single-qubit rotations.
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