Duplicate gates with higher-order gate functions in structured programs

[dime10]

The normal mechanism in PennyLane that "un-queues" a gate when supplied to a HOF like qml.adjoint does not work when the original and modified gate appear in different program scopes, such as across control flow segments. The reason is that Catalyst using different tapes for each section.

import pennylane as qml

@qml.qjit
@qml.qnode(qml.device("lightning.qubit", wires=1))
def circuit(b: bool):
    g = qml.H(0)

    @qml.cond(b)
    def apply():
        qml.adjoint(g)
    apply()

    return qml.state()

print(circuit(1))  # should not read [1, 0]