  This paper studies the application of the Quantum Approximate Optimization
Algorithm (QAOA) to spin-glass models with random multi-body couplings in the
limit of a large number of spins. We show that for such mixed-spin models the
performance of depth $1$ QAOA is independent of the specific instance in the
limit of infinite sized systems and we give an explicit formula for the
expected performance. We also give explicit expressions for the higher moments
of the expected energy, thereby proving that the expected performance of QAOA
concentrates.
