Drag

class Drag(duration, amp, sigma, beta, name=None)

Bases: qiskit.pulse.library.parametric_pulses.ParametricPulse

The Derivative Removal by Adiabatic Gate (DRAG) pulse is a standard Gaussian pulse with an additional Gaussian derivative component. It is designed to reduce the frequency spectrum of a normal gaussian pulse near the $|1\rangle$ - $|2\rangle$ transition, reducing the chance of leakage to the $|2\rangle$ state.

$$f(x) = Gaussian + 1j * beta * d/dx [Gaussian] = Gaussian + 1j * beta * (-(x - duration/2) / sigma^2) [Gaussian]$$

where ‘Gaussian’ is:

$$Gaussian(x, amp, sigma) = amp * exp( -(1/2) * (x - duration/2)^2 / sigma^2) )$$

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).

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

Initialize the drag pulse.

Parameters

• duration (Union[int, ParameterExpression]) – Pulse length in terms of the the sampling period dt.

• amp (Union[complex, ParameterExpression]) – The amplitude of the Drag envelope.

• sigma (Union[float, ParameterExpression]) – A measure of how wide or narrow the Gaussian peak is; described mathematically in the class docstring.

• beta (Union[float, ParameterExpression]) – The correction amplitude.

• name (Optional[str]) – Display name for this pulse envelope.

Methods

assign	Assign one parameter to a value, which can either be numeric or another parameter expression.
assign_parameters	Return a new ParametricPulse with parameters assigned.
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]

beta

The weighing factor for the Gaussian derivative component of the waveform.

Return type

Union[float, ParameterExpression]

id

Unique identifier for this pulse.

Return type

int

limit_amplitude = True

parameters

Return type

Dict[str, Any]

sigma

The Gaussian standard deviation of the pulse width.

Return type

Union[float, ParameterExpression]