dq.rx

rx(theta: ArrayLike) -> Array

Returns the $R_x(\theta)$ rotation gate.

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

Parameters

• theta (array_like of shape (...)) –

  Rotation angle $\theta$ in radians.

Returns

(array of shape (..., 2, 2)) $R_x(\theta)$ gate.

Examples

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