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The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmoriginally proposed to find approximate solutions to Combinatorial Optimizationproblems on quantum computers. However, the algorithm has also attractedinterest for sampling purposes since it was theoretically demonstrated underreasonable complexity assumptions that one layer of the algorithm alreadyengineers a probability distribution beyond what can be simulated by classicalcomputers. In this regard, a recent study has shown as well that, in universalIsing models, this global probability distribution resembles pure butthermal-like distributions at a temperature that depends on internalcorrelations of the spin model. In this work, through an interferometricinterpretation of the algorithm, we extend the theoretical derivation of theamplitudes of the eigenstates, and the Boltzmann distributions generated bysingle-layer QAOA. We also review the implications that this behavior has fromboth a practical and fundamental perspective.

Connection between single-layer Quantum Approximate Optimization Algorithm interferometry and thermal distributions sampling