How are the infinite dimensional operators such as (Displacement, Rotation, X and P operators) and states (coherent state, displaced squeezed states) represented in a finite dimensional truncated Fock Backend?
I require the exact matrix elements of X and P in a truncated Fock space (for a single qumode) in order to make theoretical predictions to test simulations run in the Fock backend.
Hey @Omar_Ibna_Nazim!
A lot of heavy calculations are diverted to another software package we have called thewalrus: GitHub - XanaduAI/thewalrus: A library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling.. The displacement operator is one of them. In the fock representation, it’s calculated using a recurrence relation: https://github.com/XanaduAI/thewalrus/blob/master/thewalrus/fock_gradients.py#L48.
Xgate also gets decomposed into a displacement operation (see here: https://github.com/XanaduAI/strawberryfields/blob/master/strawberryfields/ops.py#L1540)
Pgate gets decomposed into an Sgate and an Rgate (see here: https://github.com/XanaduAI/strawberryfields/blob/master/strawberryfields/ops.py#L1728)
As far as getting matrix elements go, let me get back to you!
For getting the matrix representation of operators in the Fock basis, most of that is off-loaded to the thewalrus:
https://the-walrus.readthedocs.io/en/latest/code/fock_gradients.html
I recommend installing thewalrus and exploring! Let me know if this helps 