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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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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 2ⁿ ×2ⁿ 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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