  In order to understand the capabilities and limitations of quantum computers,
it is necessary to develop methods that efficiently characterize and benchmark
error channels present on these devices. In this paper, we present a method
that faithfully reconstructs a marginal (local) approximation of the effective
noise (MATEN) channel, that acts as a single layer at the end of the circuit.
We first introduce a dual map framework that allows us to analytically derive
expectation values of observables with respect to noisy circuits. These
findings are supported by numerical simulations of the quantum approximate
optimization algorithm (QAOA) that also justify the MATEN, even in the presence
of non-local errors that occur during a circuit. Finally, we demonstrate the
performance of the method on Rigetti's Aspen-9 quantum computer for QAOA
circuits up to six qubits, successfully predicting the observed measurements on
a majority of the qubits.
