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qiskit.pulse.library.GaussianSquareDrag

GaussianSquareDrag(duration, amp, sigma, beta, width=None, angle=0.0, risefall_sigma_ratio=None, name=None, limit_amplitude=None)

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A square pulse with a Drag shaped rise and fall

This pulse shape is similar to GaussianSquare but uses Drag for its rise and fall instead of Gaussian. The addition of the DRAG component of the rise and fall is sometimes helpful in suppressing the spectral content of the pulse at frequencies near to, but slightly offset from, the fundamental frequency of the drive. When there is a spectator qubit close in frequency to the fundamental frequency, suppressing the drive at the spectator’s frequency can help avoid unwanted excitation of the spectator.

Exactly one of the risefall_sigma_ratio and width parameters has to be specified.

If risefall_sigma_ratio is not None and width is None:

risefall=risefall_sigma_ratio×sigmawidth=duration−2×risefall\begin{split}\text{risefall} &= \text{risefall\_sigma\_ratio} \times \text{sigma}\\ \text{width} &= \text{duration} - 2 \times \text{risefall}\end{split}

If width is not None and risefall_sigma_ratio is None:

risefall=duration−width2\text{risefall} = \frac{\text{duration} - \text{width}}{2}

Gaussian g(x,c,σ)g(x, c, σ) and lifted gaussian g′(x,c,σ)g'(x, c, σ) curves can be written as:

g(x,c,σ)=exp⁡(−12(x−c)2σ2)g′(x,c,σ)=g(x,c,σ)−g(−1,c,σ)1−g(−1,c,σ)\begin{split}g(x, c, σ) &= \exp\Bigl(-\frac12 \frac{(x - c)^2}{σ^2}\Bigr)\\ g'(x, c, σ) &= \frac{g(x, c, σ)-g(-1, c, σ)}{1-g(-1, c, σ)}\end{split}

From these, the lifted DRAG curve d′(x,c,σ,β)d'(x, c, σ, β) can be written as

d′(x,c,σ,β)=g′(x,c,σ)×(1+1j×β×(−x−cσ2))d'(x, c, σ, β) = g'(x, c, σ) \times \Bigl(1 + 1j \times β \times \Bigl(-\frac{x - c}{σ^2}\Bigr)\Bigr)

The lifted gaussian square drag pulse f′(x)f'(x) is defined as:

f′(x)={A×d′(x,risefall,sigma,beta)x<risefallArisefall≤x<risefall+widthA××d′(x−(risefall+width),risefall,sigma,beta)risefall+width≤x\begin{split}f'(x) &= \begin{cases} \text{A} \times d'(x, \text{risefall}, \text{sigma}, \text{beta}) & x < \text{risefall}\\ \text{A} & \text{risefall} \le x < \text{risefall} + \text{width}\\ \text{A} \times \times d'( x - (\text{risefall} + \text{width}), \text{risefall}, \text{sigma}, \text{beta} ) & \text{risefall} + \text{width} \le x \end{cases}\\\end{split}

where A=amp×exp⁡(i×angle)\text{A} = \text{amp} \times \exp\left(i\times\text{angle}\right).

Parameters

  • duration (Union[int, ParameterExpression]) – Pulse length in terms of the sampling period dt.
  • amp (Union[float, ParameterExpression]) – The amplitude of the DRAG rise and fall and of the square pulse.
  • sigma (Union[float, ParameterExpression]) – A measure of how wide or narrow the DRAG risefall is; see the class docstring for more details.
  • beta (Union[float, ParameterExpression]) – The DRAG correction amplitude.
  • width (Union[float, ParameterExpression, None]) – The duration of the embedded square pulse.
  • angle (Union[float, ParameterExpression, None]) – The angle in radians of the complex phase factor uniformly scaling the pulse. Default value 0.
  • risefall_sigma_ratio (Union[float, ParameterExpression, None]) – The ratio of each risefall duration to sigma.
  • 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.

Return type

SymbolicPulse

Returns

ScalableSymbolicPulse instance.

Raises

PulseError – When width and risefall_sigma_ratio are both empty or both non-empty.

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