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	Plot the interpolated envelope of pulse.
get_waveform	Return a Waveform with samples filled according to the formula that the pulse represents and the parameter values it contains.
is_parameterized	Return True iff the instruction is parameterized.
validate_parameters	Validate parameters.

Attributes

amp

The Gaussian amplitude.

Return type

Union[complex, ParameterExpression]

id

Unique identifier for this pulse.

Return type

int

limit_amplitude = 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]