System-Bath Functions

We provide several functions specifically for the system-bath analysis. The following is a list of system-bath functions that are included in the Noise App. Please refer to the Bath Fitter documentation or its Python API documentation for additional system-bath tools.

• coupling_to_spectral_function: A tool that takes a spin-boson system-bath and creates the effective spectral function seen by the system. The couplings in the system-bath correspond to \(g_{ism}\). If the spectral function is unphysical, the closest solution according to the Frobenius norm is returned.

• spectral_function_to_coupling: The opposite of the previous function. It takes the spectral function seen by a spin system and constructs a collection of bosonic baths that would produce that spectral function. The constructed bosonic baths can include cross-correlations in the coupling. If the spectral function is unphysical, the closest solution according to the Frobenius norm is returned.

• SpinBRNoiseOperator: A helper class that can represent the spectral function for a spin-system for defined frequencies. Includes cross-correlations.

  • Functions:
    • set: Set the component of the spectral function corresponding to the PauliProduct given by key.
    • get: Get the component of the spectral function corresponding to the PauliProduct given by key.
    • frequencies: Return the frequencies for which the spectral functions are defined.
    • get_spectral_function_matrix: Gets the matrix of the spectral function of a spin-system at a specific energy index. A real spectral function must be symmetric in the coupling indices. The method will fail if the SpinBRNoiseOperator is not symmetric. The output of this function will be of size 3n, as there are three possible coupling types for each index: X, Y, and Z.
    • resample: Resamples the SpinBRNoiseOperator on a new set of frequencies. The SpinBRNoiseOperator defined on the old frequencies is interpolated for the new frequencies. The interpolated values are taken as the new values of the spectral function for the new frequencies.