  In order to assess whether quantum resources can provide an advantage over
classical computation, it is necessary to characterize and benchmark the
non-classical properties of quantum algorithms in a practical manner. In this
paper, we show that using measurements in no more than 3 out of the possible
$3^N$ bases, one can not only reconstruct the single-qubit reduced density
matrices and measure the ability to create coherent superpositions, but also
possibly verify entanglement across all $N$ qubits participating in the
algorithm. We introduce a family of generalized Bell-type observables for which
we establish an upper bound to the expectation values in fully separable states
by proving a generalization of the Cauchy-Schwarz inequality, which may serve
of independent interest. We demonstrate that a subset of such observables can
serve as entanglement witnesses for QAOA-MaxCut states, and further argue that
they are especially well tailored for this purpose by defining and computing an
entanglement potency metric on witnesses. A subset of these observables also
certify, in a weaker sense, the entanglement in GHZ states, which share the
$\mathbb{Z}_2$ symmetry of QAOA-MaxCut. The construction of such witnesses
follows directly from the cost Hamiltonian to be optimized, and not through the
standard technique of using the projector of the state being certified. It may
thus provide insights to construct similar witnesses for other variational
algorithms prevalent in the NISQ era. We demonstrate our ideas with
proof-of-concept experiments on the Rigetti Aspen-9 chip for ansatze containing
up to 24 qubits.
