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Quantum Approximate Optimization Algorithm Pseudo-Boltzmann States.

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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… Click to show full 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.

Keywords: optimization algorithm; approximate optimization; boltzmann states; pseudo boltzmann; quantum approximate

Journal Title: Physical review letters
Year Published: 2022

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