# Drag¶

class Drag(duration: Union[int, ParameterExpression], amp: Union[complex, float, ParameterExpression], sigma: Union[float, ParameterExpression], beta: Union[float, ParameterExpression], angle: Optional[Union[float, ParameterExpression]] = None, name: Optional[str] = None, limit_amplitude: Optional[bool] = None)[source]

Bases: object

The Derivative Removal by Adiabatic Gate (DRAG) pulse is a standard Gaussian pulse with an additional Gaussian derivative component and lifting applied.

It can be calibrated either to reduce the phase error due to virtual population of the $$|2\rangle$$ state during the pulse or to reduce the frequency spectrum of a standard Gaussian pulse near the $$|1\rangle\leftrightarrow|2\rangle$$ transition, reducing the chance of leakage to the $$|2\rangle$$ state.

$\begin{split}g(x) &= \exp\Bigl(-\frac12 \frac{(x - \text{duration}/2)^2}{\text{sigma}^2}\Bigr)\\ g'(x) &= \text{A}\times\frac{g(x)-g(-1)}{1-g(-1)}\\ f(x) &= g'(x) \times \Bigl(1 + 1j \times \text{beta} \times \Bigl(-\frac{x - \text{duration}/2}{\text{sigma}^2}\Bigr) \Bigr), \quad 0 \le x < \text{duration}\end{split}$

where $$g(x)$$ is a standard unlifted Gaussian waveform, $$g'(x)$$ is the lifted Gaussian waveform, and $$\text{A} = \text{amp} \times \exp\left(i\times\text{angle}\right)$$.

References

Create new pulse instance.

Parameters
• duration -- Pulse length in terms of the sampling period dt.

• amp -- The magnitude of the amplitude of the DRAG envelope. Complex amp support will be deprecated.

• sigma -- A measure of how wide or narrow the Gaussian peak is; described mathematically in the class docstring.

• beta -- The correction amplitude.

• angle -- The angle of the complex amplitude of the DRAG envelope. Default value 0.

• name -- Display name for this pulse envelope.

• limit_amplitude -- If True, then limit the amplitude of the waveform to 1. The default is True and the amplitude is constrained to 1.

Returns

ScalableSymbolicPulse instance.

Attributes

alias = 'Drag'