new_quadratic_sequence

qctrlopencontrols.new_quadratic_sequence(duration, inner_offset_count, outer_offset_count, pre_post_rotation=False, name=None)

Creates the quadratic sequence.

Parameters

duration (float) – The total duration of the sequence $\tau$ (in seconds).
inner_offset_count (int) – Number of inner $Z_{\pi}$ pulses $n_1$ .
outer_offset_count (int) – Number of outer $X_{\pi}$ pulses $n_2$ .
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.

The quadratic sequence ¹ is parameterized by duration $\tau$ , number of inner offsets $n_1$ , and number of outer offsets $n_2$ . The outer sequence consists of $n_2$ pulses of type $X_{\pi}$ , which partition the time-domain into $n_2+1$ sub-intervals on which inner sequences consisting of $n_1$ pulses of type $Z_{\pi}$ are nested. The total number of offsets is $n = n_1 + n_2(n_1 + 1)$ .

The pulse times for outer sequence $(X_{\pi}^1, \cdots, X_{\pi}^{n_2})$ are defined according to the Uhrig sequence for $t \in [0, \tau]$ . The $j$ -th $X_{\pi}$ pulse, therefore has timing offset defined by

t_x^j = \tau \sin^2 \left[ \frac{j \pi}{2(n_2 + 1)} \right] \;,

where $j = 1, \cdots, n_2$ . On each sub-interval defined by the outer sequence, an inner sequence $(Z_{\pi}^1, \cdots, Z_{\pi}^{n_1})$ is implemented. The pulse times for the inner sequences are also defined according to the Uhrig sequence. The $k$ -th pulse of the $j$ -th inner sequence has timing offset defined by

t_z(k, j) = (t_x^j - t_x^{j - 1}) \sin^2 \left[ \frac{k \pi} {2 (n_1 + 1)} \right] + t_{x}^{j - 1} \;,

where $k = 1, \cdots, n_1$ and $j = 1, \cdots, n_2 + 1$ .

References

[1] J. R. West, B. H. Fong, and D. A. Lidar, Physical Review Letters 104, 130501 (2010).

Parameters

Returns

Return type

SEE ALSO

Notes

References