Comparison of Hyperplane Rounding for Max-Cut and Quantum Approximate Optimization Algorithm over Certain Regular Graph Families

• URL: http://arxiv.org/abs/2509.24108v1
• Date: Sun, 28 Sep 2025 23:00:28 GMT
• Title: Comparison of Hyperplane Rounding for Max-Cut and Quantum Approximate Optimization Algorithm over Certain Regular Graph Families
• Authors: Reuben Tate, Swati Gupta,
• Abstract summary: Goemans-Williamson algorithm for approximating the Max-Cut achieves at most a 0.912-approximation.<n>We explore construction of challenging instances computationally by perturbing edge weights, which may be of independent interest.
• Score: 0.9699101045941679
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There is a strong interest in finding challenging instances of NP-hard problems, from the perspective of showing quantum advantage. Due to the limits of near-term NISQ devices, it is moreover useful if these instances are small. In this work, we identify two graph families ($|V|<1000$) on which the Goemans-Williamson algorithm for approximating the Max-Cut achieves at most a 0.912-approximation. We further show that, in comparison, a recent quantum algorithm, Quantum Approximate Optimization Algorithm (depth $p=1$), is a 0.592-approximation on Karloff instances in the limit ($n \to \infty$), and is at best a $0.894$-approximation on a family of strongly-regular graphs. We further explore construction of challenging instances computationally by perturbing edge weights, which may be of independent interest, and include these in the CI-QuBe github repository.

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