Quantum Approximate Optimization Algorithm Pseudo-Boltzmann States

Authors: Diez-Valle, Pablo; Porras, Diego; Garcia-Ripoll, Juan Jose

Journal: PHYSICAL REVIEW LETTERS

Publication date: 2023/02/02

DOI: 10.1103/PhysRevLett.130.050601

Abstract: In this Letter, we provide analytical and numerical evidence that the single-layer quantum approximate optimization algorithm 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.