new_xy_concatenated_sequence

qctrlopencontrols.new_xy_concatenated_sequence(duration, concatenation_order, pre_post_rotation=False, name=None)[source]

Creates the \(XY\)-concatenated sequence.

Parameters
  • duration (float) – The total duration of the sequence \(\tau\) (in seconds).

  • concatenation_order (int, optional) – The number of concatenation of base sequence \(l\).

  • pre_post_rotation (bool, optional) – If True, a \(X_{\pi/2}\) rotation is added at the start and end of the sequence. Defaults to False.

  • name (string, optional) – Name of the sequence. Defaults to None.

Returns

The \(XY\)-concatenated sequence.

Return type

DynamicDecouplingSequence

Notes

The \(XY\)-concatenated sequence 1 is constructed by recursively concatenating control sequence structures. It’s parameterized by the concatenation order \(l\) and the duration of the total sequence \(\tau\). Let the \(l\)-th order of concatenation be denoted as \(C_l(\tau)\). In this scheme, zeroth order concatenation of duration \(\tau\) is defined as free evolution over a period of \(\tau\). Using the notation \({\mathcal 1}(\tau)\) to represent free evolution over duration \(\tau\), the the base sequence is:

\[C_0(\tau) = {\mathcal 1}(\tau) \;.\]

The \(l\)-th order \(XY\)-concatenated sequence can be recursively defined as

\[C_l(\tau) = C_{l - 1}(\tau / 4) X_{\pi} C_{l - 1}(\tau / 4) Y_{\pi} C_{l - 1}(\tau / 4) X_{\pi} C_{l - 1}(\tau / 4) Y_{\pi} \;.\]

References

1

K. Khodjasteh and D. A. Lidar, Physical Review Letters 95, 180501 (2005).