What should we add?

I think it would be a good idea to add a Transpiler pass that computes the light cone of an observable. For those who are not familiar, a light cone is the set of gates in a circuit that affect the measurement of a subset of the qubits. For example, if you have a shallow EfficientSU2 ansatz with pairwise entanglement on 127 qubits and you are trying to measure an expectation value on a single qubit you can typically reduce the circuit to a 20 qubit circuit (just making up the number, in practice it depends). I use it a lot in my research and I know of other researchers that do it as well. We all typically have a naive implementation of it, but it would be a powerful tool to have one that handles edge cases directly implemented into Qiskit.

I can take care of this issue as I already have code that does it. Before tacking this problem, however, it would be wise to first implement the proposal in #12790 to allow for computation of light cones also in parameterized circuits.