CUBO-to-QUBO Conversion: Reducing Cubic Formulations to Quadratic Formulations

Quadratic Unconstrained Binary Optimization (QUBO) models are defined by quadratic expressions composed of binary variables, each taking a value of either 0 or 1. The objective of the QUBO problem is to find an optimal assignment of these binary variables that minimizes the value of the QUBO model. The QUBO problem has attracted significant research interest due to its versatility in reformulating various NP-complete problems and its potential for efficiently finding heuristic solutions through quantum annealing. This paper focuses on converting Cubic Unconstrained Binary Optimization (CUBO) problems, defined by cubic expressions, into equivalent QUBO models. Through this conversion, CUBO problems can be solved using quantum annealing. Since the important NP-hard problem 3-SAT can be straightforwardly represented as a CUBO problem, investigating the conversion from CUBO to QUBO models is a meaningful endeavor.