# 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`

.

### Returns

The quadratic sequence.

### Return type

### SEE ALSO

## Notes

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).