QAOA pseudo-Boltzmann states
Pablo Díez-Valle · DIGITAL.CSIC (Spanish National Research Council (CSIC)) · 2022
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 with Gaussian perturbations. We find that these pseudo-Boltzmann states can not be efficiently simulated on classical computers according to state-of-art techniques, and we relate this distribution to the optimization potential of QAOA. 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.