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June 12, 2026Open Access

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

Key Points

This research aims to investigate the average-case hardness of the Quantum Hypergraph Max-Cut problem via the Quantum Overlap Gap Property.
Analyzed stable quantum algorithms and local quantum algorithms to establish hardness results.
Identified concrete conditions for the failure of known quantum algorithms in achieving near-optimal solutions.
Demonstrated a weak hardness result relevant to a wide class of stable quantum algorithms.
Established a strong hardness result for a more limited class of local quantum algorithms.

Abstract

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.

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Mikhail Mints (Wed,) studied this question.

synapsesocial.com/papers/6a2ba2f68101cf8926f01b96 https://doi.org/https://doi.org/10.7907/tgg7-nh54

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