qctrlopencontrols.new_corpse_in_scrofulous_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)Creates a CORPSE concatenated within SCROFULOUS (CORPSE in SCROFULOUS) driven control.
CORPSE in SCROFULOUS driven controls are robust to both low-frequency noise sources that perturb
the amplitude of the control field and low-frequency dephasing noise.
rabi_rotation (float ) – The total Rabi rotation θ \theta θ π / 4 \pi/4 π /4 π / 2 \pi/2 π /2 π \pi π maximum_rabi_rate (float ) – The maximum Rabi frequency Ω m a x \Omega_{\mathrm max} Ω m a x azimuthal_angle (float , optional ) – The azimuthal angle ϕ \phi ϕ name (str , optional ) – An optional string to name the control. Defaults to None.
The driven control { ( δ t n , Ω n , ϕ n , Δ n ) } \{(\delta t_n, \Omega_n, \phi_n, \Delta_n)\} {( δ t n , Ω n , ϕ n , Δ n )}
DrivenControl
new_corpse_controlnew_scrofulous_control
A CORPSE in SCROFULOUS driven control 1
δ t n \delta t_n δ t n Ω n \Omega_n Ω n ϕ n \phi_n ϕ n Δ n \Delta_n Δ n Γ 1 θ 1 / Ω m a x \Gamma^{\theta_1}_1/\Omega_{\mathrm max} Γ 1 θ 1 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 1 \phi+\phi_1 ϕ + ϕ 1 0 0 0 Γ 2 θ 1 / Ω m a x \Gamma^{\theta_1}_2/\Omega_{\mathrm max} Γ 2 θ 1 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 1 + π \phi+\phi_1+\pi ϕ + ϕ 1 + π 0 0 0 Γ 3 θ 1 / Ω m a x \Gamma^{\theta_1}_3/\Omega_{\mathrm max} Γ 3 θ 1 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 1 \phi+\phi_1 ϕ + ϕ 1 0 0 0 Γ 1 θ 2 / Ω m a x \Gamma^{\theta_2}_1/\Omega_{\mathrm max} Γ 1 θ 2 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 2 \phi+\phi_2 ϕ + ϕ 2 0 0 0 Γ 2 θ 2 / Ω m a x \Gamma^{\theta_2}_2/\Omega_{\mathrm max} Γ 2 θ 2 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 2 + π \phi+\phi_2+\pi ϕ + ϕ 2 + π 0 0 0 Γ 3 θ 2 / Ω m a x \Gamma^{\theta_2}_3/\Omega_{\mathrm max} Γ 3 θ 2 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 2 \phi+\phi_2 ϕ + ϕ 2 0 0 0 Γ 1 θ 3 / Ω m a x \Gamma^{\theta_3}_1/\Omega_{\mathrm max} Γ 1 θ 3 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 3 \phi+\phi_3 ϕ + ϕ 3 0 0 0 Γ 2 θ 3 / Ω m a x \Gamma^{\theta_3}_2/\Omega_{\mathrm max} Γ 2 θ 3 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 3 + π \phi+\phi_3+\pi ϕ + ϕ 3 + π 0 0 0 Γ 3 θ 3 / Ω m a x \Gamma^{\theta_3}_3/\Omega_{\mathrm max} Γ 3 θ 3 / Ω m a x Ω m a x \Omega_{\mathrm max} Ω m a x ϕ + ϕ 3 \phi+\phi_3 ϕ + ϕ 3 0 0 0
where
θ 1 = θ 3 = s i n c − 1 [ 2 cos ( θ / 2 ) π ] θ 2 = π ϕ 1 = ϕ 3 = cos − 1 [ − π cos ( θ 1 ) 2 θ 1 sin ( θ / 2 ) ] ϕ 2 = ϕ 1 − cos − 1 ( − π 2 θ 1 )
\begin{align}
\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} \left(-\frac{\pi}{2\theta_1}\right)
\end{align}
θ 1 θ 2 ϕ 1 ϕ 2 = θ 3 = sinc − 1 [ π 2 cos ( θ /2 ) ] = π = ϕ 3 = cos − 1 [ 2 θ 1 sin ( θ /2 ) − π cos ( θ 1 ) ] = ϕ 1 − cos − 1 ( − 2 θ 1 π ) (with s i n c ( x ) = sin ( x ) / x \mathrm{sinc}(x)=\sin(x)/x sinc ( x ) = sin ( x ) / x
Γ 1 θ ′ = 2 π + θ ′ 2 − sin − 1 [ sin ( θ ′ / 2 ) 2 ] Γ 2 θ ′ = 2 π − 2 sin − 1 [ sin ( θ ′ / 2 ) 2 ] Γ 3 θ ′ = θ ′ 2 − sin − 1 [ sin ( θ ′ / 2 ) 2 ]
\begin{align}
\Gamma^{\theta'}_1 &=
2\pi + \frac{\theta'}{2} - \sin^{-1} \left[ \frac{\sin(\theta'/2)}{2}\right] \\
\Gamma^{\theta'}_2 &=
2\pi - 2\sin^{-1} \left[ \frac{\sin(\theta'/2)}{2}\right] \\
\Gamma^{\theta'}_3 &= \frac{\theta'}{2} - \sin^{-1} \left[ \frac{\sin(\theta'/2)}{2}\right]
\end{align}
Γ 1 θ ′ Γ 2 θ ′ Γ 3 θ ′ = 2 π + 2 θ ′ − sin − 1 [ 2 sin ( θ ′ /2 ) ] = 2 π − 2 sin − 1 [ 2 sin ( θ ′ /2 ) ] = 2 θ ′ − sin − 1 [ 2 sin ( θ ′ /2 ) ] are the CORPSE angles corresponding to each SCROFULOUS angle
θ ′ ∈ { θ 1 , θ 2 , θ 3 } \theta'\in\{\theta_1,\theta_2,\theta_3\} θ ′ ∈ { θ 1 , θ 2 , θ 3 }
