From Maximum Cut to Maximum Independent Set

TL;DR

This paper explores the relationship between Max-Cut and Maximum Independent Set problems, demonstrating that Max-Cut/Ising solvers can effectively approximate MIS, with significant improvements on random graphs and coding theory benchmarks.

Contribution

It introduces a novel approach of using Max-Cut/Ising solvers to approximate MIS, enhancing performance on specific graph and coding theory problems.

Findings

Improved approximation of the independence number in Erd ext{o}s-Rényi graphs.

Perfect performance on a coding theory benchmark.

Potential for developing quantum algorithms for MIS and coding problems.

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.