# Ry operation

Warning

This documentation refers to the Classic QDK, which has been replaced by the Modern QDK.

Please see https://aka.ms/qdk.api for the API documentation for the Modern QDK.

Namespace: Microsoft.Quantum.Intrinsic

Package: Microsoft.Quantum.Type2.Core

Applies a rotation about the $y$-axis by a given angle.

```
operation Ry (theta : Double, qubit : Qubit) : Unit is Adj + Ctl
```

## Description

\begin{align} R_y(\theta) \mathrel{:=} e^{-i \theta \sigma_y / 2} = \begin{bmatrix} \cos \frac{\theta}{2} & -\sin \frac{\theta}{2} \\ \sin \frac{\theta}{2} & \cos \frac{\theta}{2} \end{bmatrix}. \end{align}

## Input

### theta : Double

Angle in radians about which the qubit is to be rotated.

### qubit : Qubit

Qubit to which the gate should be applied.

## Output : Unit

## Remarks

Equivalent to:

```
R(PauliY, theta, qubit);
```

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