RX gate

The RX gate, a rotation about X by any angle: matrix, effect on the basis states, the rx() call in Python and JS, and its IonQ native-gate form.

The RX gate rotates a qubit about the X axis of the Bloch sphere by an angle $\theta$ . It acts on one qubit and takes one parameter, $\theta$ in radians. The Circuit panel draws it as Rx(θ) with the angle shown as a multiple of π. Measured straight after it, a qubit that started as 0 reads 1 with probability $\sin^2(\theta/2)$ : never at $\theta = 0$ , half the time at $\theta = \pi/2$ , always at $\theta = \pi$ .

Kets such as $\vert 0 \rangle$ name the basis states and rotations are described on the Bloch sphere; the qubits lesson introduces both.

Call

Where	Call
Python	`qc.rx(θ, qubit)`
JS	`circuit.rx(θ, qubit)`
Qiskit class	`RXGate`
Controlled form	`crx(θ, control, target)`

Matrix

RX(\theta) = \begin{pmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}

rx(π) is an X gate and rx(π/2) is a √X gate, both up to a global phase.

Effect on basis states

Input	Output
$\vert 0 \rangle$	$\cos\frac{\theta}{2}\vert 0 \rangle - i\sin\frac{\theta}{2}\vert 1 \rangle$
$\vert 1 \rangle$	$-i\sin\frac{\theta}{2}\vert 0 \rangle + \cos\frac{\theta}{2}\vert 1 \rangle$

Measured straight after rx(θ), a qubit that started in $\vert 0 \rangle$ reads 1 with probability $\sin^2(\theta/2)$ : 0 at $\theta = 0$ , one half at $\theta = \pi/2$ , certainty at $\theta = \pi$ .

Inverse

The inverse of rx(θ) is rx(-θ).

Usage

from math import pi
from qiskit import QuantumCircuit

qc = QuantumCircuit(1, 1)
qc.rx(pi / 3, 0)
qc.measure(0, 0)

import { QuantumCircuit } from 'qiskit';

const circuit = QuantumCircuit(1, 1);
circuit.rx(Math.PI / 3, 0);
circuit.measure(0, 0);

Over many shots about a quarter of them read 1: $\sin^2(\pi/6) = 0.25$ .

On IonQ hardware

RX is not a native gate for a general angle, because the native pulses GPi and GPi2 have fixed angles of π and π/2. An arbitrary rx(θ) compiles to two GPi2 pulses with a virtual Z of angle θ between them. The special angles are cheaper: rx(±π/2) is a single GPi2 and rx(π) is a single GPi. See How your circuit is compiled.

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