In my research, I need to define an operator e^{i\theta\sigma_x\otimes\hat{p}}, which is hybrid qubit-qumode gate. How to apply it in pennylane?

It seems that one should first claim
“class Custom(CVOperation)”, or “class Custom(Operation)”. But either can be used to define a hybrid qubit-qumode operator.

Does pennylane would support such operators in future? Since e^{it\sigma_x\otimes\hat{p}} is an Hamiltonian evolution of a spin-momentum coupling, it is important for simulating quantum physics.

At the moment, a hybrid qubit-qumode gate isn’t supported, for two kind of separate reasons:

We currently don’t have a PennyLane plugin/device/backend that can simulate hybrid qubit-qumode quantum operations.

Even with a PennyLane device that allows hybrid qubit-qumode gates, PennyLane calculates the analytic gradients via different methods for either type of quantum operation — we would need to ensure that the current gradient formulas we use generalize to the qubit-qumode case, and that the code will allow this. My feeling is this should definitely be doable.

As a fallback, if 1. is implemented but 2. isn’t, PennyLane’s numerical differentiation/finite-difference gradient approximations should still work.

This would be a interesting addition to PennyLane though, and would be great to have