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arXiv · 2504.11120

Improved approximation ratios for the Quantum Max-Cut problem on general, triangle-free and bipartite graphs

Sander Gribling·Lennart Sinjorgo·Renata Sotirov
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Abstract

We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that corresponds to $G$. We provide a sharpened analysis of the currently best-known QMC approximation algorithm for general graphs. This algorithm achieves an approximation ratio of $0.599$, which our analysis improves to $0.603$. Additionally, we propose two new approximation algorithms for the QMC problem on triangle-free and bipartite graphs, that achieve approximation ratios of $0.61383$ and $0.8162$, respectively. These are the best-known approximation ratios for their respective graph classes.

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Sander Gribling, Lennart Sinjorgo, Renata Sotirov. 2025-04-15. Improved approximation ratios for the Quantum Max-Cut problem on general, triangle-free and bipartite graphs. https://arxiv.org/abs/2504.11120

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