diff --git a/qctrlopencontrols/driven_controls/predefined.py b/qctrlopencontrols/driven_controls/predefined.py index 59d2571..7bb3f5f 100644 --- a/qctrlopencontrols/driven_controls/predefined.py +++ b/qctrlopencontrols/driven_controls/predefined.py @@ -123,7 +123,7 @@ def new_primitive_control( rabi_rotation : float The total Rabi rotation :math:`\theta` to be performed by the driven control. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -141,7 +141,7 @@ def new_primitive_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` + :math:`\theta/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` """ _validate_rabi_parameters( @@ -174,7 +174,7 @@ def new_bb1_control( rabi_rotation : float The total Rabi rotation :math:`\theta` to be performed by the driven control. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -192,10 +192,10 @@ def new_bb1_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_*`, :math:`0` - :math:`2\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+3\phi_*`,:math:`0` - :math:`\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_*`, :math:`0` + :math:`\theta/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_*`, :math:`0` + :math:`2\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+3\phi_*`,:math:`0` + :math:`\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_*`, :math:`0` where @@ -206,7 +206,7 @@ def new_bb1_control( ---------- .. [#] `S. Wimperis, Journal of Magnetic Resonance, Series A 109, 2 (1994). `_ - """ + """ # pylint: disable=line-too-long _validate_rabi_parameters( rabi_rotation=rabi_rotation, maximum_rabi_rate=maximum_rabi_rate @@ -255,7 +255,7 @@ def new_sk1_control( rabi_rotation : float The total Rabi rotation :math:`\theta` to be performed by the driven control. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -273,9 +273,9 @@ def new_sk1_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`2\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi-\phi_*`, :math:`0` - :math:`2\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_*`, :math:`0` + :math:`\theta/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`2\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi-\phi_*`, :math:`0` + :math:`2\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_*`, :math:`0` where @@ -288,7 +288,7 @@ def new_sk1_control( `_ .. [#] `K. R. Brown, A. W. Harrow, and I. L. Chuang, Physical Review A 72, 039905 (2005). `_ - """ + """ # pylint: disable=line-too-long _validate_rabi_parameters( rabi_rotation=rabi_rotation, maximum_rabi_rate=maximum_rabi_rate @@ -334,7 +334,7 @@ def new_scrofulous_control( The total Rabi rotation :math:`\theta` to be performed by the driven control. Must be either :math:`\pi/4`, :math:`\pi/2`, or :math:`\pi`. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -352,20 +352,21 @@ def new_scrofulous_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta_1/\Omega_{\rm max}`, :math:`\Omega_\rm{max}`, :math:`\phi+\phi_1`, :math:`0` - :math:`\theta_2/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_2`, :math:`0` - :math:`\theta_3/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_3`, :math:`0` + :math:`\theta_1/\Omega_{\mathrm max}`, :math:`\Omega_\mathrm{max}`, :math:`\phi+\phi_1`, :math:`0` + :math:`\theta_2/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_2`, :math:`0` + :math:`\theta_3/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_3`, :math:`0` where .. math:: - \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), + \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} and :math:`\mathrm{sinc}(x)=\sin(x)/x` is the unnormalized sinc function. @@ -373,7 +374,7 @@ def new_scrofulous_control( ---------- .. [#] `H. K. Cummins, G. Llewellyn, and J. A. Jones, Physical Review A 67, 042308 (2003). `_ - """ + """ # pylint: disable=line-too-long _validate_rabi_parameters( rabi_rotation=rabi_rotation, maximum_rabi_rate=maximum_rabi_rate @@ -449,7 +450,7 @@ def new_corpse_control( rabi_rotation : float The total Rabi rotation :math:`\theta` to be performed by the driven control. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -467,18 +468,19 @@ def new_corpse_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta_1/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`\theta_2/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\pi`, :math:`0` - :math:`\theta_3/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` + :math:`\theta_1/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`\theta_2/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\pi`, :math:`0` + :math:`\theta_3/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` where .. math:: - \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] + \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] + \end{align} - \theta_3 &= \frac{\theta}{2} - \sin^{-1} \left[ \frac{\sin(\theta/2)}{2}\right]. References ---------- @@ -486,7 +488,7 @@ def new_corpse_control( `_ .. [#] `H. K. Cummins, G. Llewellyn, and J. A. Jones, Physical Review A 67, 042308 (2003). `_ - """ + """ # pylint: disable=line-too-long _validate_rabi_parameters( rabi_rotation=rabi_rotation, maximum_rabi_rate=maximum_rabi_rate @@ -534,7 +536,7 @@ def new_corpse_in_bb1_control( rabi_rotation : float The total Rabi rotation :math:`\theta` to be performed by the driven control. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -557,23 +559,22 @@ def new_corpse_in_bb1_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta_1/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`\theta_2/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\pi`, :math:`0` - :math:`\theta_3/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_*`, :math:`0` - :math:`2\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+3\phi_*`, :math:`0` - :math:`\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_*`, :math:`0` + :math:`\theta_1/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`\theta_2/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\pi`, :math:`0` + :math:`\theta_3/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_*`, :math:`0` + :math:`2\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+3\phi_*`, :math:`0` + :math:`\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_*`, :math:`0` where .. math:: - \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). + \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 ---------- @@ -581,7 +582,7 @@ def new_corpse_in_bb1_control( Japan 82, 1 (2012). `_ .. [#] `C. Kabytayev, T. J. Green, K. Khodjasteh, M. J. Biercuk, L. Viola, and K. R. Brown, Physical Review A 90, 012316 (2014). `_ - """ + """ # pylint: disable=line-too-long _validate_rabi_parameters( rabi_rotation=rabi_rotation, maximum_rabi_rate=maximum_rabi_rate @@ -641,7 +642,7 @@ def new_corpse_in_sk1_control( rabi_rotation : float The total Rabi rotation :math:`\theta` to be performed by the driven control. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -664,22 +665,21 @@ def new_corpse_in_sk1_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta_1/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`\theta_2/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\pi`, :math:`0` - :math:`\theta_3/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`2\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi-\phi_*`, :math:`0` - :math:`2\pi/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi+\phi_*`, :math:`0` + :math:`\theta_1/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`\theta_2/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\pi`, :math:`0` + :math:`\theta_3/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`2\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi-\phi_*`, :math:`0` + :math:`2\pi/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi+\phi_*`, :math:`0` where .. math:: - \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). + \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 ---------- @@ -687,7 +687,7 @@ def new_corpse_in_sk1_control( Japan 82, 1 (2012). `_ .. [#] `C. Kabytayev, T. J. Green, K. Khodjasteh, M. J. Biercuk, L. Viola, and K. R. Brown, Physical Review A 90, 012316 (2014). `_ - """ + """ # pylint: disable=line-too-long _validate_rabi_parameters( rabi_rotation=rabi_rotation, maximum_rabi_rate=maximum_rabi_rate @@ -746,7 +746,7 @@ def new_corpse_in_scrofulous_control( The total Rabi rotation :math:`\theta` to be performed by the driven control. Must be either :math:`\pi/4`, :math:`\pi/2`, or :math:`\pi`. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -769,46 +769,48 @@ def new_corpse_in_scrofulous_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\Gamma^{\theta_1}_1/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_1}_1/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_1`", :math:`0` - :math:`\Gamma^{\theta_1}_2/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_1}_2/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_1+\pi`", :math:`0` - :math:`\Gamma^{\theta_1}_3/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_1}_3/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_1`", :math:`0` - :math:`\Gamma^{\theta_2}_1/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_2}_1/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_2`", :math:`0` - :math:`\Gamma^{\theta_2}_2/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_2}_2/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_2+\pi`", :math:`0` - :math:`\Gamma^{\theta_2}_3/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_2}_3/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_2`", :math:`0` - :math:`\Gamma^{\theta_3}_1/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_3}_1/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_3`", :math:`0` - :math:`\Gamma^{\theta_3}_2/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_3}_2/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_3+\pi`", :math:`0` - :math:`\Gamma^{\theta_3}_3/\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, " + :math:`\Gamma^{\theta_3}_3/\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, " :math:`\phi+\phi_3`", :math:`0` where .. math:: - \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) + \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} (with :math:`\mathrm{sinc}(x)=\sin(x)/x` the unnormalized sinc function) are the SCROFULOUS angles, and .. math:: - \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] - + \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} are the CORPSE angles corresponding to each SCROFULOUS angle :math:`\theta'\in\{\theta_1,\theta_2,\theta_3\}`. @@ -905,7 +907,7 @@ def new_wamf1_control( The total Rabi rotation :math:`\theta` to be performed by the driven control. Must be either :math:`\pi/4`, :math:`\pi/2`, or :math:`\pi`. maximum_rabi_rate : float - The maximum Rabi frequency :math:`\Omega_{\rm max}` for the driven control. + The maximum Rabi frequency :math:`\Omega_{\mathrm max}` for the driven control. azimuthal_angle : float, optional The azimuthal angle :math:`\phi` for the rotation. Defaults to 0. name : str, optional @@ -923,12 +925,12 @@ def new_wamf1_control( .. csv-table:: :header: :math:`\\delta t_n`, :math:`\\Omega_n`, :math:`\\phi_n` , :math:`\\Delta_n` - :math:`\theta_+/4\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` - :math:`\theta_+/4\Omega_{\rm max}`, :math:`\Omega_{\rm max}\theta_-/\theta_+`," + :math:`\theta_+/4\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` + :math:`\theta_+/4\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}\theta_-/\theta_+`," :math:`\phi`", :math:`0` - :math:`\theta_+/4\Omega_{\rm max}`, :math:`\Omega_{\rm max}\theta_-/\theta_+`, " + :math:`\theta_+/4\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}\theta_-/\theta_+`, " :math:`\phi`", :math:`0` - :math:`\theta_+/4\Omega_{\rm max}`, :math:`\Omega_{\rm max}`, :math:`\phi`, :math:`0` + :math:`\theta_+/4\Omega_{\mathrm max}`, :math:`\Omega_{\mathrm max}`, :math:`\phi`, :math:`0` where :math:`\theta_\pm = \theta+2\pi k_\theta\pm \delta_\theta`, and the integer :math:`k_\theta` and offset :math:`\delta_\theta` are optimized numerically in order to maximize diff --git a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py index a01a6e5..59ab6f9 100644 --- a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py +++ b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py @@ -614,14 +614,15 @@ def new_walsh_sequence( function [#]_, which is defined as .. math:: - R_j(x) := {\rm sgn}\left[\sin(2^j \pi x)\right] \;, \quad\; x \in [0, 1]\;, \; j \geq 0 \;. + R_j(x) := {\mathrm sgn}\left[\sin(2^j \pi x)\right] \;, + \quad\; x \in [0, 1]\;, \; j \geq 0 \;. The :math:`j`-th Rademacher function :math:`R_j(x)` is thus a periodic square wave switching :math:`2^{j-1}` times between :math:`\pm 1` over the interval :math:`[0, 1]`. The Walsh - function of Paley order :math:`k` is denoted :math:`{\rm PAL}_k(x)` and defined as + function of Paley order :math:`k` is denoted :math:`{\mathrm PAL}_k(x)` and defined as .. math:: - {\rm PAL}_k(x) = \Pi_{j = 1}^m R_j(x)^{b_j} \;, \quad\; x \in [0, 1] \;. + {\mathrm PAL}_k(x) = \Pi_{j = 1}^m R_j(x)^{b_j} \;, \quad\; x \in [0, 1] \;. where :math:`(b_m, b_{m-1}, \cdots, b_1)` is the binary representation of :math:`k`. That is @@ -634,7 +635,7 @@ def new_walsh_sequence( The :math:`k`-th order Walsh sequence [#]_ is then defined by .. math:: - y(t) = {\rm PAL}_k(t / \tau) \; + y(t) = {\mathrm PAL}_k(t / \tau) \; with offset times :math:`\{t_j / \tau\}` defined at the switching times of the Walsh function.