# new_x_concatenated_sequence¶

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

Creates the $$X$$-concatenated sequence.

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

• concatenation_order (int) – The number of concatenation of base sequence.

• 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 $$X$$-concatenated sequence.

Return type

DynamicDecouplingSequence

Notes

The $$X$$-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 $$X$$-concatenated sequence can be recursively defined as

$C_l(\tau) = C_{l - 1}(\tau / 2) X_{\pi} C_{l - 1}(\tau / 2) X_{\pi} \;.$

References

1

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