Efficient QUBO transformation for Higher Degree Pseudo Boolean Functions

Abstract: Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is useful to have a method for transforming higher degree pseudo-Boolean problems to QUBO format. The standard transformation approach requires additional auxiliary variables supported by penalty terms for each higher degree term. This paper improves on the existing cubic-to-quadratic transformation approach by minimizing the number of additional variables as well as penalty coefficient. Extensive experimental testing on Max 3-SAT modeled as QUBO shows a near 100% reduction in the subproblem size used for minimization of the number of auxiliary variables.