Drag

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

Bases: SymbolicPulse

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.

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

where \(g(x)\) is a standard unlifted Gaussian waveform and \(g'(x)\) is the lifted Gaussian waveform.

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.

Create new pulse instance.

Parameters

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

• 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.

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.

Return type

Expr

duration

envelope

Return symbolic expression for the pulse envelope.

Return type

Expr

id

Unique identifier for this pulse.

Return type

int

limit_amplitude = True

name

parameters

Return type

Dict[str, Any]

pulse_type

Return display name of the pulse shape.

Return type

str

valid_amp_conditions

Return symbolic expression for the pulse amplitude constraints.

Return type

Expr