new_scrofulous_control
- qctrlopencontrols.new_scrofulous_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)[source]
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 \(\{(\delta t_n, \Omega_n, \phi_n, \Delta_n)\}\).
- Return type:
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
\[ \begin{align}\begin{aligned}\theta_1 &= \theta_3 = \mathrm{sinc}^{-1} \left[\frac{2\cos (\theta/2)}{\pi}\right]\\\theta_2 &= \pi\\\phi_1 &= \phi_3 = \cos^{-1}\left[ \frac{-\pi\cos(\theta_1)}{2\theta_1\sin(\theta/2)}\right]\\\phi_2 &= \phi_1 - \cos^{-1} (-\pi/2\theta_1),\end{aligned}\end{align} \]and \(\mathrm{sinc}(x)=\sin(x)/x\) is the unnormalized sinc function.
References