dq.ry

ry(theta: ArrayLike) -> Array

Returns the \(R_y(\theta)\) rotation gate.

It is defined by $$ R_y(\theta) = \begin{pmatrix} \cos(\theta/2) & -\sin(\theta/2) \\ \sin(\theta/2) & \cos(\theta/2) \end{pmatrix} $$

Parameters

• theta (array_like of shape (...)) –

  Rotation angle \(\theta\) in radians.

Returns

(array of shape (..., 2, 2)) \(R_y(\theta)\) gate.

Examples

>>> dq.ry(jnp.pi)
Array([[-0.+0.j, -1.+0.j],
       [ 1.+0.j, -0.+0.j]], dtype=complex64)
>>> dq.ry([0, jnp.pi/4, jnp.pi/3, jnp.pi/2, jnp.pi]).shape
(5, 2, 2)