degree reduction

To utilize a quantum annealing system such as D-Wave's to solve a graph coloring problem,
it is necessary to convert the utility polynomial into a quadratic polynomial in binary variables.
This is called QUBO (quadratic unconstrained binary optimization) problem.
In any degree reduction process, we need to introduce auxiliary variables,
and more variables we have in the QUBO problem, less likely a
quantum annealing system can find an optimal solution.
The current degree reduction methods applies to monomials.