Instantiation with controlled VariableUnitaryGate

[martinanibbi]

I would like to use instatiation on a parametrized circuit which includes controlled operations:

circuit = Circuit(4)
V1 = VariableUnitaryGate(3)
# control on 0
circuit.append_gate(ControlledGate(V1, num_controls=1), [0,1,2,3])

circuit.instantiate(
            unitary,
            method='qfactor',
            diff_tol_a=1e-12,   # Stopping criteria for distance change
            diff_tol_r=1e-10,    # Relative criteria for distance change
            dist_tol=1e-12,     # Stopping criteria for distance
            max_iters=100000,   # Maximum number of iterations
            min_iters=1000,     # Minimum number of iterations
            slowdown_factor=0,   # Larger numbers slowdown optimization
            # to avoid local minima
        )

I currently get the following error:

Cannot instantiate circuit with qfactor because the following gates are not locally optimizable: Controlled(VariableUnitaryGate(3, (2, 2, 2))).

When using minimization the code produces a similar error.

From my understanding, the problem is that ControlledGate is not a LocallyOptimizableUnitary.
Is there a way to circumnavigate this issue, is it a missing feature or is it simply impossible to use controlled parametrized gates with the instantiation method?

[edyounis]

It is hard to say if it is possible or impossible, but it is not currently implemented. If the instantiation is more important than using Qfactor, you can swap the VariableUnitaryGate for a PauliGate, which should work with minimization.

[edyounis]

I think it should be possible to make a ControlledGate locally optimizable conditioned on the inner gate being locally optimizable.