new_corpse_in_sk1_control

qctrlopencontrols.new_corpse_in_sk1_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)

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 θ\theta to be performed by the driven control.
  • maximum_rabi_rate (float) – The maximum Rabi frequency Ωmax\Omega_{\mathrm max} for the driven control.
  • azimuthal_angle (float , optional) – The azimuthal angle ϕ\phi for the rotation. Defaults to 0.
  • name (str , optional) – An optional string to name the control. Defaults to None.

Returns

The driven control {(δtn,Ωn,ϕn,Δn)}\{(\delta t_n, \Omega_n, \phi_n, \Delta_n)\}.

Return type

DrivenControl

SEE ALSO

new_corpse_control, new_sk1_control

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:

δtn\delta t_nΩn\Omega_nϕn\phi_nΔn\Delta_n
θ1/Ωmax\theta_1/\Omega_{\mathrm max}Ωmax\Omega_{\mathrm max}ϕ\phi00
θ2/Ωmax\theta_2/\Omega_{\mathrm max}Ωmax\Omega_{\mathrm max}ϕ+π\phi+\pi00
θ3/Ωmax\theta_3/\Omega_{\mathrm max}Ωmax\Omega_{\mathrm max}ϕ\phi00
2π/Ωmax2\pi/\Omega_{\mathrm max}Ωmax\Omega_{\mathrm max}ϕ−ϕ∗\phi-\phi_*00
2π/Ωmax2\pi/\Omega_{\mathrm max}Ωmax\Omega_{\mathrm max}ϕ+ϕ∗\phi+\phi_*00

where

θ1=2π+θ2−sin⁡−1[sin⁡(θ/2)2]θ2=2π−2sin⁡−1[sin⁡(θ/2)2]θ3=θ2−sin⁡−1[sin⁡(θ/2)2]ϕ∗=cos⁡−1(−θ4π) \begin{align} \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{align}

References

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