Quantum Approximate Optimization Algorithm pseudo-Boltzmann states

TL;DR

This paper demonstrates that single-layer QAOA on Ising models produces thermal-like states that are hard to simulate classically, with a temperature linked to universal energy correlations.

Contribution

It provides analytical and numerical evidence connecting QAOA states to pseudo-Boltzmann states and highlights their classical intractability.

Findings

QAOA states resemble thermal states with specific temperature dependence.

Classical simulation of these states is inefficient due to rapid mixing conditions.

A universal correlation governs the temperature and energy relationships in these states.

Abstract

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.