A Refined Algorithm For the EPR model

• URL: http://arxiv.org/abs/2506.08547v1
• Date: Tue, 10 Jun 2025 08:12:14 GMT
• Title: A Refined Algorithm For the EPR model
• Authors: Wenxuan Tao, Fen Zuo,
• Abstract summary: Two groups independently develop specific algorithms for the highest-energy state with approximation ratio $frac1+sqrt54approx.809$.<n>Here we try to refine one of the two algorithms by devising homogeneous/quasi-homogeneous fractional matchings.<n>For irregular graphs, we show such a refinement could still guarantee nice performance if the fractional matchings are chosen properly.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The Einstein-Podolsky-Rosen~(EPR) model is an analogous model of the anti-ferromagnetic Heisenberg model or the equivalent quantum maximum-cut problem, proposed by R. King two years ago. Adjacent qubits in the model prefer symmetric EPR/Bell parings rather than the antisymmetric one, in order to maximize the energy. Recently, two groups independently develop specific algorithms for the highest-energy state with approximation ratio $\frac{1+\sqrt{5}}{4}\approx.809$, based on maximum fractional matchings. Here we try to refine one of the two algorithms by devising homogeneous/quasi-homogeneous fractional matchings, with the aim to distribute quantum entanglement as much as possible. For regular graphs $G_d$, we immediately obtain increasing approximation ratios $r_d$ with $r_2=\frac{3+\sqrt{5}}{6}\approx.872$. For irregular graphs, we show such a refinement could still guarantee nice performance if the fractional matchings are chosen properly.

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