  The Quantum Approximate Optimization Algorithm (QAOA) requires that circuit
parameters are determined that allow one to sample from high-quality solutions
to combinatorial optimization problems. Such parameters can be obtained using
either costly outer-loop optimization procedures and repeated calls to a
quantum computer or, alternatively, via analytical means. In this work we
demonstrate that if one knows the probability density function describing how
the objective function of a problem is distributed, that the calculation of the
expectation of such a problem Hamiltonian under a Grover-driven, QAOA-prepared
state can be performed independently of system size. Such calculations can help
deliver insights into the performance of and predictability of angles in QAOA
in the limit of large problem sizes, in particular, for the number partitioning
problem.
