The Quantum Overlap Gap Property and Algorithmic Hardness for the Quantum Hypergraph Max-Cut Problem

In this work, we analyze the average-case hardness of the Quantum Hypergraph Max-Cut problem using the theoretical framework of the Quantum Overlap Gap Property (QOGP). We establish two main results: a weak hardness result for a wide class of stable quantum algorithms, and a strong hardness result for a much more restricted class of local quantum algorithms. We apply these results to establish concrete conditions under which known quantum algorithms fail to produce near-optimal solutions for this problem.