This issue has been tagged for a bounty during unitaryHACK

It would be great to have a compiler in Strawberry Fields that:

• Applies to arbitrary programs, containing both Gaussian and non-Gaussian operations
• Combines the Gaussian operations into a single symplectic operation, by multiplying together their symplectic forms.

This could significantly reduce overhead during computation.

As an example, consider the following diagram:

This circuit contains a mixture of Gaussian gates (green) and non-Gaussian gates (red). While the cross-Kerr gate in the middle of the circuit prevents us from combining all Gaussian gates, we can create two Gaussian gates, S1 and S2:

Note that this grouping is not unique! We could have potentially included the second beamsplitter within S1, rather than S2 as we did.