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Table of Contents

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

  1. Gambetta, J. M., Motzoi, F., Merkel, S. T. & Wilhelm, F. K. Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator. Phys. Rev. A 83, 012308 (2011).

  1. F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm Phys. Rev. Lett. 103, 110501 – Published 8 September 2009.

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'