dq.rz

rz(theta: ArrayLike) -> Array

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

It is defined by $$R_z(\theta) = \begin{pmatrix} e^{-i\theta/2} & 0 \\ 0 & e^{i\theta/2} \end{pmatrix}$$

Parameters

• theta (array_like of shape (...)) –

  Rotation angle $\theta$ in radians.

Returns

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

Examples

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