69 lines
3.2 KiB
Plaintext
69 lines
3.2 KiB
Plaintext
---
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title: GaussianSquare
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description: API reference for qiskit.pulse.library.GaussianSquare
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.pulse.library.GaussianSquare
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---
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# GaussianSquare
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<Class id="qiskit.pulse.library.GaussianSquare" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.22/qiskit/pulse/library/symbolic_pulses.py" signature="GaussianSquare(duration: Union[int, qiskit.circuit.parameterexpression.ParameterExpression], amp: Union[complex, qiskit.circuit.parameterexpression.ParameterExpression], sigma: Union[float, qiskit.circuit.parameterexpression.ParameterExpression], width: Optional[Union[float, qiskit.circuit.parameterexpression.ParameterExpression]] = None, risefall_sigma_ratio: Optional[Union[float, qiskit.circuit.parameterexpression.ParameterExpression]] = None, name: Optional[str] = None, limit_amplitude: Optional[bool] = None)" modifiers="class">
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Bases: `object`
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A square pulse with a Gaussian shaped risefall on both sides lifted such that its first sample is zero.
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Exactly one of the `risefall_sigma_ratio` and `width` parameters has to be specified.
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If `risefall_sigma_ratio` is not None and `width` is None:
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$$
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\begin{split}\text{risefall} &= \text{risefall_sigma_ratio} \times \text{sigma}\\
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\text{width} &= \text{duration} - 2 \times \text{risefall}\end{split}
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$$
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If `width` is not None and `risefall_sigma_ratio` is None:
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$$
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\text{risefall} = \frac{\text{duration} - \text{width}}{2}
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$$
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In both cases, the lifted gaussian square pulse $f'(x)$ is defined as:
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$$
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\begin{split}f'(x) &= \begin{cases} \exp\biggl(-\frac12 \frac{(x - \text{risefall})^2}{\text{sigma}^2}\biggr) & x < \text{risefall}\\
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1 & \text{risefall} \le x < \text{risefall} + \text{width}\\
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\exp\biggl(-\frac12 \frac{{\bigl(x - (\text{risefall} + \text{width})\bigr)}^2} {\text{sigma}^2} \biggr) & \text{risefall} + \text{width} \le x \end{cases}\\
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f(x) &= \text{amp} \times \frac{f'(x) - f'(-1)}{1-f'(-1)}, \quad 0 \le x < \text{duration}\end{split}
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$$
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where $f'(x)$ is the gaussian square waveform without lifting or amplitude scaling.
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Create new pulse instance.
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**Parameters**
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* **duration** – Pulse length in terms of the sampling period dt.
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* **amp** – The amplitude of the Gaussian and of the square pulse.
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* **sigma** – A measure of how wide or narrow the Gaussian risefall is; see the class docstring for more details.
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* **width** – The duration of the embedded square pulse.
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* **risefall\_sigma\_ratio** – The ratio of each risefall duration to sigma.
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* **name** – Display name for this pulse envelope.
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* **limit\_amplitude** – If `True`, then limit the amplitude of the waveform to 1. The default is `True` and the amplitude is constrained to 1.
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**Returns**
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SymbolicPulse instance.
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**Raises**
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[**PulseError**](pulse#qiskit.pulse.PulseError "qiskit.pulse.PulseError") – When width and risefall\_sigma\_ratio are both empty or both non-empty.
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## Attributes
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### alias
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<Attribute id="qiskit.pulse.library.GaussianSquare.alias" attributeValue="'GaussianSquare'" />
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</Class>
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