new_corpse_in_sk1_control
- qctrlopencontrols.new_corpse_in_sk1_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)[source]
Creates a CORPSE concatenated within SK1 (CORPSE in SK1) driven control.
CORPSE in SK1 driven controls are robust to both low-frequency noise sources that perturb the amplitude of the control field and low-frequency dephasing noise.
- Parameters:
rabi_rotation (float) – The total Rabi rotation \(\theta\) to be performed by the driven control.
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:
See also
Notes
A CORPSE in SK1 driven control [1] [2] consists of an SK1 control with the first segment replaced by a CORPSE control, which yields five segments:
\(\delta t_n\)
\(\Omega_n\)
\(\phi_n\)
\(\Delta_n\)
\(\theta_1/\Omega_{\rm max}\)
\(\Omega_{\rm max}\)
\(\phi\)
\(0\)
\(\theta_2/\Omega_{\rm max}\)
\(\Omega_{\rm max}\)
\(\phi+\pi\)
\(0\)
\(\theta_3/\Omega_{\rm max}\)
\(\Omega_{\rm max}\)
\(\phi\)
\(0\)
\(2\pi/\Omega_{\rm max}\)
\(\Omega_{\rm max}\)
\(\phi-\phi_*\)
\(0\)
\(2\pi/\Omega_{\rm max}\)
\(\Omega_{\rm max}\)
\(\phi+\phi_*\)
\(0\)
where
\[ \begin{align}\begin{aligned}\theta_1 &= 2\pi + \frac{\theta}{2} - \sin^{-1} \left[ \frac{\sin(\theta/2)}{2}\right]\\\theta_2 &= 2\pi - 2\sin^{-1} \left[ \frac{\sin(\theta/2)}{2}\right]\\\theta_3 &= \frac{\theta}{2} - \sin^{-1} \left[ \frac{\sin(\theta/2)}{2}\right]\\\phi_* &= \cos^{-1} \left( -\frac{\theta}{4\pi} \right).\end{aligned}\end{align} \]References