Hi,

I am wondering if it’s possible to compute fidelity between two bosonic states (linear combinations of Gaussians). I know this can be done with Gaussian states, but not linear combinations of them.

I first thought about combining the vectors of means and covariance matrices from the Gaussians in the linear combination to get a single Gaussian, but now I am not sure I have enough data to do something like that.

Another method I’m thinking of is to compare each Gaussian of a set to its “corresponding” Gaussian of the other set. But here, I don’t know what the correct ordering is to carry on this comparison.

For some more context: I am comparing output GKP states from a CSUM circuit and its teleported version, both of which run using the bosonic backend.

Previously, I had been converting these output states into a Fock basis representation (using density matrix) but this process takes a while (and I want to compare this circuit for several choices of circuit parameters).

Now I am wondering if it’s possible to compare the output states using their linear combination of Gaussians expressions and not having to convert them to the Fock basis.

Thanks, and let me know if you need more information!