qctrlopencontrols.new_wamf1_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)

Creates a first-order Walsh amplitude-modulated filter (WAMF1) driven control.

WAMF1 driven controls are robust to low-frequency dephasing noise.


  • rabi_rotation (float) – The total Rabi rotation θ\theta to be performed by the driven control. Must be either π/4\pi/4, π/2\pi/2, or π\pi
  • maximum_rabi_rate (float) – The maximum Rabi frequency Ωmax\Omega_{\rm max}
  • azimuthal_angle (float , optional) – The azimuthal angle ϕ\phi
  • name (str , optional) – An optional string to name the control. Defaults to None.


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

Return type



A WAMF1 1 driven control consists of four control segments:

$\delta t_n$$\Omega_n$$\phi_n$$\Delta_n$
$\theta_+/4\Omega_{\rm max}$$\Omega_{\rm max}$$\phi$$0$
$\theta_+/4\Omega_{\rm max}$$\Omega_{\rm max}\theta_-/\theta_+$$\phi$$0$
$\theta_+/4\Omega_{\rm max}$$\Omega_{\rm max}\theta_-/\theta_+$$\phi$$0$
$\theta_+/4\Omega_{\rm max}$$\Omega_{\rm max}$$\phi$$0$

where θ±=θ+2πkθ±δθ\theta_\pm = \theta+2\pi k_\theta\pm \delta_\theta, and the integer kθk_\theta and offset δθ\delta_\theta are optimized numerically in order to maximize the suppression of dephasing noise. Note that the optimal values depend only on the rotation angle θ\theta

This implementation supports θ{π/4,π/2,π}\theta\in\{\pi/4,\pi/2,\pi\}


[1] H. Ball and M. J. Biercuk, EPJ Quantum Technology 2, 11 (2015).

Was this useful?