Graph.gaussian_convolution_kernel(std, offset=0)

Create a convolution kernel representing a normalized Gaussian.

Use this kernel to allow angular frequencies in the range roughly determined by its width, and progressively suppress components outside that range.


  • std (float or Tensor) – Standard deviation σ\sigma
  • offset (float or Tensor , optional) – Center μ\mu


A node representing a Gaussian function to use in a convolution.

Return type



Graph.convolve_pwc : Create an Stf by convolving a Pwc with a kernel.

Graph.sinc_convolution_kernel : Create a convolution kernel representing the sinc function.


The Gaussian kernel that this node represents is defined as:

K(t)=e(tμ)2/(2σ2)2πσ2. K(t) = \frac{e^{-(t-\mu)^2/(2\sigma^2)}}{\sqrt{2\pi\sigma^2}}.

In the frequency domain, this Gaussian has standard deviation ωc=σ1\omega_c= \sigma^{-1}. The filter it represents therefore passes angular frequencies roughly in the range [ωc,ωc][-\omega_c, \omega_c]

For more information on Stf nodes see the Working with time-dependent functions in Boulder Opal topic.


Filter a signal by convolving it with a Gaussian kernel.

>>> gaussian_kernel = graph.gaussian_convolution_kernel(std=1.0, offset=3.0)
>>> gaussian_kernel
<ConvolutionKernel: operation_name="gaussian_convolution_kernel">
>>> signal
<Pwc: name="alpha", operation_name="pwc_signal", value_shape=(), batch_shape=()>
>>> filtered_signal = graph.convolve_pwc(pwc=signal, kernel=gaussian_kernel)
>>> filtered_signal
<Stf: operation_name="convolve_pwc", value_shape=(), batch_shape=()>

Refer to the How to characterize a transmission line using a qubit as a probe user guide to find the example in context.

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