rotations 1 qubit 1 parameter
$x$ Rotation
Rotation about the $x$ axis of the Bloch sphere.
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.
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis. Each parameter has a slider; play runs through the family along the path of the Quirk link ($\theta = 2\pi t$).
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
SDK support
How to call this gate in each framework. Hover a ⓘ for a note; the support matrix compares every gate at once.
| SDK | Name |
|---|---|
| Qiskit | qiskit.circuit.library.RXGate |
| PennyLane | pennylane.RX |
| Cirq | cirq.Rx |
| Q# | Std.Intrinsic.Rx |
| PyQuil | pyquil.gates.RX |
| Braket | braket.circuits.gates.Rx |
| BQSKit | bqskit.ir.gates.RXGate |
| Qibo | qibo.gates.RX |
| pytket | pytket.circuit.OpType.Rx ⓘ |
| Stim | — |
| OpenQASM | stdgates.inc: rx |