  We propose and demonstrate a unified hierarchical method to measure $n$-point
correlation functions that can be applied to driven, dissipative, or otherwise
open or non-equilibrium quantum systems. In this method, the time evolution of
the system is repeatedly interrupted by interacting an ancilla qubit with the
system through a controlled operation, and measuring the ancilla immediately
afterwards. We discuss the robustness of this method as compared to other
ancilla-based interferometric techniques (such as the Hadamard test), and
highlight its advantages for near-term quantum simulations of open quantum
systems. We implement the method on a quantum computer in order to measure
single-particle Green's functions of a driven-dissipative fermionic system.
This work shows that dynamical correlation functions for driven-dissipative
systems can be robustly measured with near-term quantum computers.
