new_x_concatenated_sequence

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

Creates the $X$

Parameters

duration (float) – The total duration of the sequence $\tau$
concatenation_order (int) – The number of concatenation of base sequence.
pre_post_rotation (bool , optional) – If True, a $X_{\pi/2}$ False.
name (string , optional) – Name of the sequence. Defaults to None.

The $X$ 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 $\tau$

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

The $l$ -th order $X$

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).

Parameters

Returns

Return type

SEE ALSO

Notes

References