new_sk1_control

qctrlopencontrols.new_sk1_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 Solovay-Kitaev (SK1) driven control.

SK1 driven controls are robust to low-frequency noise sources that perturb the amplitude of the control field.

Parameters
  • rabi_rotation (float) – The total Rabi rotation \(\theta\) to be performed by the driven control.

  • 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

An SK1 driven control 1 2 consists of three control segments:

\(\delta t_n\)

\(\Omega_n\)

\(\phi_n\)

\(\Delta_n\)

\(\theta/\Omega_{\rm max}\)

\(\Omega_{\rm max}\)

\(\phi\)

\(0\)

\(2\pi/\Omega_{\rm max}\)

\(\Omega_{\rm max}\)

\(\phi-\phi_*\)

\(0\)

\(2\pi/\Omega_{\rm max}\)

\(\Omega_{\rm max}\)

\(\phi+\phi_*\)

\(0\)

where

\[\phi_* = \cos^{-1} \left( -\frac{\theta}{4\pi} \right).\]

References

1

K. R. Brown, A. W. Harrow, and I. L. Chuang, Physical Review A 70, 052318 (2004).

2

K. R. Brown, A. W. Harrow, and I. L. Chuang, Physical Review A 72, 039905 (2005).