# gaussian_pulse_pwc¶

The Boulder Opal Toolkits are currently in beta phase of development. Breaking changes may be introduced.

gaussian_pulse_pwc(duration, segment_count, amplitude, width=None, center_time=None, drag=None, flat_duration=None, segmentation='UNIFORM', *, name=None)

Create a Pwc representing a Gaussian pulse.

Parameters
• duration (float) – The duration of the signal, $$T$$.

• segment_count (int) – The number of segments in the PWC. Must be at least four.

• amplitude (float or complex or Tensor) – The amplitude of the Gaussian pulse, $$A$$. It must either be a scalar or contain a single element.

• width (float or Tensor, optional) – The standard deviation of the Gaussian pulse, $$\sigma$$. It must either be a scalar or contain a single element. Defaults to $$T/10$$ or $$(T-t_\mathrm{flat})/10$$ if flat_duration is passed.

• center_time (float, optional) – The center of the Gaussian pulse, $$t_0$$. Defaults to half of the given value of the duration, $$T/2$$.

• drag (float or Tensor, optional) – The DRAG parameter, $$\beta$$. If passed, it must either be a scalar or contain a single element. Defaults to no DRAG correction.

• flat_duration (float, optional) – The amount of time to remain constant after the peak of the Gaussian, $$t_\mathrm{flat}$$. If passed, it must be positive and less than the duration. Defaults to None, in which case no constant part is added to the Gaussian pulse.

• segmentation (SegmentationType) – The type of segmentation for the signal. With a “MINIMAL” segmentation, most of the segments are placed in the non-constant parts of the signal. Defaults to “UNIFORM”, in which case the segments are uniformly distributed along the signal’s duration.

• name (str, optional) – The name of the node.

Returns

The sampled Gaussian pulse. If no flat duration is passed then the pulse is evenly sampled between $$0$$ and $$T$$. If one is passed, the flat part of the pulse is described by one or two segments (depending on the values of center_time and segment_count), and the rest of the pulse is sampled with the remaining segments.

Return type

Pwc

signals.cosine_pulse_pwc()

Create a Pwc representing a cosine pulse.

signals.gaussian_pulse_stf()

Corresponding operation with Stf output.

signals.sech_pulse_pwc()

Create a Pwc representing a hyperbolic secant pulse.

signals.square_pulse_pwc()

Create a Pwc representing a square pulse.

Notes

The Gaussian pulse is defined as

$\begin{split}\mathop{\mathrm{Gaussian}}(t) = \begin{cases} A \left(1-\frac{i\beta (t-t_1)}{\sigma^2}\right) \exp \left(- \frac{(t-t_1)^2}{2\sigma^2} \right) &\mathrm{if} \quad t < t_1=t_0- t_\mathrm{flat}/2\\ A &\mathrm{if} \quad t_0-t_\mathrm{flat}/2 \le t < t_0+t_\mathrm{flat}/2 \\ A \left(1-\frac{i\beta (t-t_2)}{\sigma^2}\right) \exp \left(- \frac{(t-t_2)^2}{2\sigma^2} \right) &\mathrm{if} \quad t > t_2=t_0+t_\mathrm{flat}/2 \end{cases} .\end{split}$

If the flat duration is zero (the default setting), this reduces to

$\mathop{\mathrm{Gaussian}}(t) = A \left(1-\frac{i\beta (t-t_0)}{\sigma^2}\right) \exp \left(- \frac{(t-t_0)^2}{2\sigma^2} \right) .$

Examples

Define a Gaussian PWC pulse.

>>> graph.signals.gaussian_pulse_pwc(
...     duration=3.0,
...     segment_count=100,
...     amplitude=1.0,
...     name="gaussian",
... )
<Pwc: name="gaussian", operation_name="discretize_stf", value_shape=(), batch_shape=()>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["gaussian"])
>>> result.output["gaussian"]
[
{'duration': 0.03, 'value': 4.7791e-06},
{'duration': 0.03, 'value': 7.8010e-06},
...
{'duration': 0.03, 'value': 7.8010e-06},
{'duration': 0.03, 'value': 4.7791e-06}
]


Define a flat-top Gaussian PWC pulse with a DRAG correction with minimal segmentation.

>>> graph.signals.gaussian_pulse_pwc(
...     duration=3.0,
...     segment_count=100,
...     amplitude=1.0,
...     width=0.2,
...     center_time=1.5,
...     drag=0.1,
...     flat_duration=0.2,
...     segmentation="MINIMAL",
...     name="gaussian_drag",
... )
<Pwc: name="gaussian_drag", operation_name="time_concatenate_pwc", value_shape=(), batch_shape=()>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["gaussian_drag"])
>>> result.output["gaussian_drag"]
[
{'duration': 0.0285, 'value': (3.7655e-11+1.3044e-10j)},
{'duration': 0.0285, 'value': (1.0028e-10+3.4026e-10j)},
...
{'duration': 0.0285, 'value': (1.0028e-10-3.4026e-10j)},
{'duration': 0.0285, 'value': (3.7655e-11-1.3044e-10j)}
]


Define a Gaussian pulse with optimizable parameters.

>>> amplitude = graph.optimization_variable(
...     count=1, lower_bound=0, upper_bound=2.*np.pi, name="amplitude"
... )
>>> width = graph.optimization_variable(
...     count=1, lower_bound=0.1, upper_bound=2., name="width"
... )
>>> drag = graph.optimization_variable(
...     count=1, lower_bound=0, upper_bound=1., name="drag"
... )
>>> graph.signals.gaussian_pulse_pwc(
...     duration=3.0,
...     segment_count=100,
...     amplitude=amplitude,
...     width=width,
...     drag=drag,
...     name="gaussian",
... )
<Pwc: name="gaussian", operation_name="discretize_stf", value_shape=(), batch_shape=()>