Quantum Approximate Optimization Algorithm Pseudo-Boltzmann States

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 t...

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Bibliographic Details
Published inPhysical review letters Vol. 130; no. 5; p. 050601
Main Authors Díez-Valle, Pablo, Porras, Diego, García-Ripoll, Juan José
Format Journal Article
LanguageEnglish
Published United States 03.02.2023
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Summary: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.
ISSN:1079-7114
DOI:10.1103/PhysRevLett.130.050601