Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, it has  been known that quantum approximate optimization algorithms have limitations for certain instances to solve MAXCUT problem, at any constant level $$extract_itex$$p$$/extract_itex$$. Recently, the recursive quantum approximate optimization algorithm, which is a non-local version of quantum approximate optimization algorithm, has been proposed to overcome these limitations. However, it has been known only as numerical evidences that the recursive quantum approximate optimization algorithm outperforms the original quantum approximate optimization algorithm for specific instances. In this work, we analytically prove that the recursive quantum approximate optimization algorithm is more competitive than the original one to solve MAX-CUT problem for complete graphs.

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