A degree reduction method for an efficient QUBO formulation for the graph coloring problem

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables,...

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Bibliographic Details
Main Authors Hong, Namho, Jung, Hyunwoo, Kang, Hyosang, Lim, Hyunjin, Seol, Chaehwan, Um, Seokhyun
Format Journal Article
LanguageEnglish
Published 21.06.2023
Subjects
Physics - Quantum Physics
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Summary:We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.
DOI:10.48550/arxiv.2306.12081