  In this letter, we provide analytical and numerical evidence that the
single-layer Quantum Approximate Optimization Algorithm (QAOA) on universal
Ising spin models produces thermal-like states. We find that these
pseudo-Boltzmann states can not be efficiently simulated on classical computers
according to the general state-of-the-art condition that ensures rapid mixing
for Ising models. Moreover, we observe that the temperature depends on a hidden
universal correlation between the energy of a state and the covariance of other
energy levels and the Hamming distances of the state to those energies.
