new_wamf1_control

qctrlopencontrols.new_wamf1_control(rabi_rotation: float, maximum_rabi_rate: float, azimuthal_angle: float = 0.0, name: Optional[str] = None) → qctrlopencontrols.driven_controls.driven_control.DrivenControl[source]

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

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

Parameters
  • rabi_rotation (float) – The total Rabi rotation \(\theta\) to be performed by the driven control. Must be either \(\pi/4\), \(\pi/2\), or \(\pi\).

  • 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

DrivenControl

Notes

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

This implementation supports \(\theta\in\{\pi/4,\pi/2,\pi\}\).

References

1

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