Hi @Shawn,

Am I understanding that correctly that visualizing/having the gates of a CV system to qubit/DV system is very complicated and not yet understood?

If that is true, how else would we be able to encode a CV system into a DV system if we don’t know how the gates look?

Or is it so, that when we have a photonic QC and a qubit QC the QCs wont need gates to simulate one another?

I’d say that it’s clear what unitary we want to do, or equivalently what the transformation is that we want to perform. The difficulty is implementing the gate physically, e.g., the CNOT gate could be probabilistic for dual-rail qubits. So it really comes down to the details of how you implement the encoded gate on an actual device.

The GKP states and their seminal paper focus on going from DV to CV. But the GKP states can also be used to go the other way, right? (I am almost certain this is true just want to get confirmation)

I’m not an expert in this area, but my understanding is that the paper shows how a qubit/finite-dimensional system can be embedded in a CV system. To me I understand this to mean “going from CV to DV”. As far as I’m aware, they don’t focus on how to embed a CV system in qubits, but I haven’t read the paper in depth.

What I am not wrapping my head around is the fact there seems to be a difference between encoding a CV system to a DV system (or vice versa) and having the gates of a CV system to a DV system. How can you encode it without having gates and vice versa? The gates are at the basis of operations of a computer and without the gates, there is no computer.

I think this comes back to the question of implementation. We can define an embedding and transformations on the embedded space, but it’s the implementation details that make things a research question for practical hardware.

@Shawn, I’m quite curious on the motivation for this line of questioning? Is this just out of interest, or related to a specific goal in PennyLane?