RY gate

The RY gate rotates a qubit about the Y 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 Ry(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

Matrix

The matrix is real, so RY never introduces complex phases. ry(π) is a Y gate up to a global phase, and ry(π/2) takes $\vert 0 \rangle$ to $\vert + \rangle$, the same state an H gate produces from $\vert 0 \rangle$.

Effect on basis states

Measured straight after ry(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 ry(θ) is ry(-θ).

Usage

from math import pi
from qiskit import QuantumCircuit

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

import { QuantumCircuit } from 'qiskit';

const circuit = QuantumCircuit(1, 1);
circuit.ry(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

RY is not a native gate for a general angle. An arbitrary ry(θ) compiles to two GPi2 pulses with a virtual Z of angle θ between them. The special angles are cheaper: ry(π/2) is exactly GPi2(0.25), a single pulse, and ry(π) is a single GPi. See How your circuit is compiled.

Related

• RX gate
• RZ gate
• Y gate
• H gate
• Gate reference