any resource you could recommend on basic continuous variable information processing,
There is a some info on the SF docs page, and also a nice review article here. As well, there are a few textbooks I quite like and would recommend, “Quantum Optics: An Introduction” by Mark Fox, and “Essential Quantum Optics” by Ulf Leonhardt.
I thought having the unitary of the circuit would be enough to translated to strawberry fields but I was wrong
Looking back, I think my original answer didn’t state things very clearly. You’re correct, a unitary is a unitary, so if you have a unitary matrix you would normally run on a gate model machine, you can use SF to decompose it, and then run it in a continuous variable framework (technically, it would need to be special unitary, but it is straightforward to convert from unitary -> special unitary, it just involves multiplying by some factor of the determinant).
It’s just that the operations it will get decomposed to are not traditional multi-qubit operations like CNOT and U3, they will be the CV operations like beamsplitters. For the case of a single qubit, it lives in effectively the same space as a two-mode CV system. In both cases, operations belong to the special unitary group SU(2) and you can associate things like beamsplitters / phase shifts with RX / RY / RZ qubit operations.
is there any simple way to map a quantum circuit (just U3 and CNOT gates) into the continuous variable model?
Great question! What you point out re. U3/CNOT is correct, and in general there are ways of doing so, but it may be challenging to actually implement physically. There is a nice discussion and some references for converting “both ways” in a forum thread here that might be helpful.
Happy to answer any other questions you may have!