From Maximum Cut to Maximum Independent Set

• URL: http://arxiv.org/abs/2408.06758v2
• Date: Wed, 18 Sep 2024 08:59:57 GMT
• Title: From Maximum Cut to Maximum Independent Set
• Authors: Chuixiong Wu, Jianan Wang, Fen Zuo,
• Abstract summary: It has long been known that the Maximum Independent Set (MIS) problem could also be related to a specific Ising model. It turns out that this strategy greatly improves the approximation for the independence number of random ErdHos-R'enyi graphs. It also exhibits perfect performance on a benchmark arising from coding theory.
• Score: 7.250073177017239
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could also be related to a specific Ising model. Therefore, it would be natural to attack MIS with various Max-Cut/Ising solvers. It turns out that this strategy greatly improves the approximation for the independence number of random Erd\H{o}s-R\'{e}nyi graphs. It also exhibits perfect performance on a benchmark arising from coding theory. These results pave the way for further development of approximate quantum algorithms on MIS, and specifically on the corresponding coding problems.

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