UnitarySynthesis ignores basis_gates argument for >= 3 qubit unitaries about qiskit HOT 1 OPEN

The default synthesis plugin used by UnitarySynthesis relies on the Quantum Shannon Decomposition module in qiskit.synthesis (https://github.com/Qiskit/qiskit/blob/main/qiskit/synthesis/unitary/qsd.py) for unitaries of > 2 qubits. It currently doesn't look at any basis gates or target constraints.

At the pass level I'm not sure we can always guarantee the output synthesis is going to respect the basis_gates or target arguments as different synthesis plugins can explicitly ignore the arguments. But I think we should look at fixing this for the default plugin though because it does advertise it does respect the basis gates and target, and this issue would potentially break the synthesis translation stage plugin too.

from qiskit.