# new_x_concatenated_sequence

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

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

new_xy_concatenated_sequence

## 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

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