# new_scrofulous_control

qctrlopencontrols.new_scrofulous_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)

Creates a short composite rotation for undoing length over and under shoot (SCROFULOUS) driven control.

SCROFULOUS driven controls are robust to low-frequency noise sources that perturb the amplitude of the control field.

### Parameters

• rabi_rotation (float) – The total Rabi rotation $\theta$ to be performed by the driven control. Must be either $\pi/4$, $\pi/2$, or $\pi$.
• maximum_rabi_rate (float) – The maximum Rabi frequency $\Omega_{\rm max}$ for the driven control.
• azimuthal_angle (float , optional) – The azimuthal angle $\phi$ for the rotation. Defaults to 0.
• name (str , optional) – An optional string to name the control. Defaults to None.

### Returns

The driven control $\{(\delta t_n, \Omega_n, \phi_n, \Delta_n)\}$.

DrivenControl

## Notes

A SCROFULOUS driven control 1 consists of three control segments:

$\delta t_n$$\Omega_n$$\phi_n$$\Delta_n \theta_1/\Omega_{\rm max}$$\Omega_\rm{max}$$\phi+\phi_1$$0$
$\theta_2/\Omega_{\rm max}$$\Omega_{\rm max}$$\phi+\phi_2$$0 \theta_3/\Omega_{\rm max}$$\Omega_{\rm max}$$\phi+\phi_3$$0$

where

\theta_1 &= \theta_3 = \mathrm{sinc}^{-1} \left[\frac{2\cos (\theta/2)}{\pi}\right] \theta_2 &= \pi \phi_1 &= \phi_3 = \cos^{-1}\left[ \frac{-\pi\cos(\theta_1)}{2\theta_1\sin(\theta/2)}\right] \phi_2 &= \phi_1 - \cos^{-1} (-\pi/2\theta_1), 

and $\mathrm{sinc}(x)=\sin(x)/x$ is the unnormalized sinc function.