When I look at the definition of the Fock device, the number of shots are per default set to 0, meaning the state is exact. But, how does that make sense for non-Gaussian gates such as the Kerr Gate? Let’s say I have at least one non-gaussian gate in a circuit and I now want to determine an expectation value, but the state isn’t a Gaussian state anymore and so there is no analytical answer as to what the expectation value should be. As far as I understand…

What would be the number of shots used in this case per default?

The distinction between whether something is “analytical” or not has to do more with whether expectation values are computed via linear algebra, or via sampling from some probability distribution a finite number of times.

In both cases, you can still have inaccuracies in the final results due to things like floating-point numerical errors, imposed numerical cutoff values, etc. In particular, the accuracy of the Kerr gate is connected to how high a cutoff you are using to simulate it, irrespective of whether the final expectation values are computed analytically or estimated.