# Fidelity Operation in Gaussian Backend

Hi,

I’d like to verify if the equation used to estimate fidelity in the gaussian backend is Eq. 80 in “Gaussian quantum information” attached below:

,

where x_i denotes the vector of means and V_i denotes the covariance matrix in the gaussian states.

Thanks!

Hi @Francisco_J_Estrella it seems that you’re right. I’m confirming with someone who worked a lot with this backend though. I hope to have an answer soon!

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The equation that you posted should be the same as the one used to calculate the fidelity in the Gaussian backend. The function used to calculate it can be found here, in a package called The Walrus. As stated in the docstring, it’s an implementation of the square of Eq. 96 in ‘Gaussian states and operations - a quick reference’, Brask.

Comparing Eq. 101 in Brask, for single mode Gaussian states, with Eq. 80 in ‘Gaussian Quantum Information’, Weedbrook, et al., we should see (using some substitutions) that they are identical.