GaussianSquare

class GaussianSquare(duration, amp, sigma, width=None, risefall_sigma_ratio=None, name=None, limit_amplitude=None)

Bases: qiskit.pulse.library.parametric_pulses.ParametricPulse

A square pulse with a Gaussian shaped risefall on both sides lifted such that its first sample is zero.

Either the risefall_sigma_ratio or width parameter has to be specified.

If risefall_sigma_ratio is not None and width is None:

\begin{split}\text{risefall} &= \text{risefall\_sigma\_ratio} \times \text{sigma}\\ \text{width} &= \text{duration} - 2 \times \text{risefall}\end{split}

If width is not None and risefall_sigma_ratio is None:

\text{risefall} = \frac{\text{duration} - \text{width}}{2}

In both cases, the lifted gaussian square pulse $f'(x)$ is defined as:

\begin{split}f'(x) &= \begin{cases} \exp\biggl(-\frac12 \frac{(x - \text{risefall})^2}{\text{sigma}^2}\biggr) & x < \text{risefall}\\ 1 & \text{risefall} \le x < \text{risefall} + \text{width}\\ \exp\biggl(-\frac12 \frac{{\bigl(x - (\text{risefall} + \text{width})\bigr)}^2} {\text{sigma}^2} \biggr) & \text{risefall} + \text{width} \le x \end{cases}\\ f(x) &= \text{amp} \times \frac{f'(x) - f'(-1)}{1-f'(-1)}, \quad 0 \le x < \text{duration}\end{split}

where $f'(x)$ is the gaussian square waveform without lifting or amplitude scaling.

This pulse would be more accurately named as LiftedGaussianSquare, however, for historical and practical DSP reasons it has the name GaussianSquare.

Initialize the gaussian square pulse.

Parameters

duration (Union[int, ParameterExpression]) – Pulse length in terms of the the sampling period dt.
amp (Union[complex, ParameterExpression]) – The amplitude of the Gaussian and of the square pulse.
sigma (Union[float, ParameterExpression]) – A measure of how wide or narrow the Gaussian risefall is; see the class docstring for more details.
width (Union[float, ParameterExpression, None]) – The duration of the embedded square pulse.
risefall_sigma_ratio (Union[float, ParameterExpression, None]) – The ratio of each risefall duration to sigma.
name (Optional[str]) – Display name for this pulse envelope.
limit_amplitude (Optional[bool]) – If True, then limit the amplitude of the waveform to 1. The default is True and the amplitude is constrained to 1.

Methods

draw

GaussianSquare.draw(style=None, backend=None, time_range=None, time_unit='dt', show_waveform_info=True, plotter='mpl2d', axis=None)

Plot the interpolated envelope of pulse.

Parameters

style (Optional[Dict[str, Any]]) – Stylesheet options. This can be dictionary or preset stylesheet classes. See IQXStandard, IQXSimple, and IQXDebugging for details of preset stylesheets.
backend (Optional[BaseBackend]) – Backend object to play the input pulse program. If provided, the plotter may use to make the visualization hardware aware.
time_range (Optional[Tuple[int, int]]) – Set horizontal axis limit. Tuple (tmin, tmax).
time_unit (str) – The unit of specified time range either dt or ns. The unit of ns is available only when backend object is provided.
show_waveform_info (bool) – Show waveform annotations, i.e. name, of waveforms. Set True to show additional information about waveforms.

plotter (str) –

Name of plotter API to generate an output image. One of following APIs should be specified:

mpl2d: Matplotlib API for 2D image generation.
    Matplotlib API to generate 2D image. Charts are placed along y axis with
    vertical offset. This API takes matplotlib.axes.Axes as `axis` input.

axis and style kwargs may depend on the plotter.

axis (Optional[Any]) – Arbitrary object passed to the plotter. If this object is provided, the plotters use a given axis instead of internally initializing a figure object. This object format depends on the plotter. See plotter argument for details.

Returns

Visualization output data. The returned data type depends on the plotter. If matplotlib family is specified, this will be a matplotlib.pyplot.Figure data.

get_waveform

GaussianSquare.get_waveform()

Return a Waveform with samples filled according to the formula that the pulse represents and the parameter values it contains.

Return type

Waveform

is_parameterized

GaussianSquare.is_parameterized()

Return True iff the instruction is parameterized.

Return type

bool

validate_parameters

GaussianSquare.validate_parameters()

Validate parameters.

Raises

PulseError – If the parameters passed are not valid.

Return type

None

Attributes

amp

The Gaussian amplitude.

Return type

Union[complex, ParameterExpression]

id

Unique identifier for this pulse.

Return type

int

limit_amplitude

Default value: True

parameters

Return type

Dict[str, Any]

risefall_sigma_ratio

The duration of each risefall in terms of sigma.

Return type

Union[float, ParameterExpression]

sigma

The Gaussian standard deviation of the pulse width.

Return type

Union[float, ParameterExpression]

width

The width of the square portion of the pulse.

Return type

Union[float, ParameterExpression]

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