Beamsplitter matrix

PennyLane Help
1

Hi,

I would assume the matrix representation of beamsplitters would return matrix of size n x n where n = cutoff dimension^2 for a two qumode system. For example, when the cutoff dimension = 2, the resulting beamsplitter matrix would be 4 x 4, and when it’s 3, 9 x 9.

Is this correct or incorrect?

Thank you.

2

Hi @sophchoe,

I’m checking with the team. I’ll be back soon with an answer.

3

Hi @sophchoe!

Thank you to Robbe De Prins for helping with this answer.

I’m assuming you’re using the Fock backend. The Fock representation of a beamsplitter has the same dimensions as a 2 mode state, which is (cutoff,cutoff,cutoff,cutoff).

Every pair of consecutive dimensions corresponds to a subsystem:
image

Does this answer your question?

Maybe going through the Teleportation tutorial can help clarify this point.