gaussian_pulse_pwc

signals.gaussian_pulse_pwc(duration, segment_count, amplitude, width=None, center_time=None, drag=None, flat_duration=None, segmentation=SegmentationType.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 or None , 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 or None , 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 or None , 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 or None , 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 or None , 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

SEE ALSO

Graph.signals.cosine_pulse_pwc : Create a Pwc representing a cosine pulse.

Graph.signals.gaussian_pulse_stf : Corresponding operation with Stf output.

Graph.signals.sech_pulse_pwc : Create a Pwc representing a hyperbolic secant pulse.

Graph.signals.square_pulse_pwc : Create a Pwc representing a square pulse.

Notes

The Gaussian pulse is defined as

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

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 = bo.execute_graph(graph=graph, output_node_names="gaussian")
>>> result["output"]["gaussian"]
{
    'durations': array([0.03, 0.03, ..., 0.03, 0.03]),
    'values': array([4.77913973e-06, 7.80106730e-06, ..., 7.80106730e-06, 4.77913973e-06]),
    'time_dimension': 0
}

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="drag",
... )
<Pwc: name="drag", operation_name="time_concatenate_pwc", value_shape=(), batch_shape=()>
>>> result = bo.execute_graph(graph=graph, output_node_names="gaussian_drag")
>>> result["output"]["gaussian_drag"]
{
    'durations': array([0.02857143, 0.02857143, ..., 0.02857143, 0.02857143]),
    'values': array([3.76551948e-11+1.30448351e-10j, 1.00289674e-10+3.40268532e-10j, ...,
                     1.00289593e-10-3.40268262e-10j, 3.76551637e-11-1.30448246e-10j]),
    'time_dimension': 0
}

Define a Gaussian pulse with optimizable parameters.

>>> amplitude = graph.optimizable_scalar(
...     lower_bound=0, upper_bound=2.*np.pi, name="amplitude"
... )
>>> width = graph.optimizable_scalar(
...     lower_bound=0.1, upper_bound=2., name="width"
... )
>>> drag = graph.optimizable_scalar(
...     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=()>