GaussianSquare¶

class GaussianSquare(duration, amp, sigma, width=None, risefall_sigma_ratio=None, name=None, limit_amplitude=None)[source]¶

Bases : SymbolicPulse

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

Exactly one of the risefall_sigma_ratio and width parameters 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.

Create new pulse instance.

Paramètres

duration (Union[int, ParameterExpression]) – Pulse length in terms of 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.

Lève

PulseError – When width and risefall_sigma_ratio are both empty or both non-empty.

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

constraints¶

Return symbolic expression for the pulse parameter constraints.

Type renvoyé: Expr

duration¶

envelope¶

Return symbolic expression for the pulse envelope.

Type renvoyé: Expr

id¶

Unique identifier for this pulse.

Type renvoyé: int

limit_amplitude = True¶

name¶

parameters¶

Type renvoyé: Dict[str, Any]

pulse_type¶

Return display name of the pulse shape.

Type renvoyé: str

risefall_sigma_ratio¶: Return risefall_sigma_ratio. This is auxiliary parameter to define width.

valid_amp_conditions¶

Return symbolic expression for the pulse amplitude constraints.

Type renvoyé: Expr