  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.
