  Recent hardware advances in quantum and quantum-inspired annealers promise
substantial speedup for solving NP-hard combinatorial optimization problems
compared to general-purpose computers. These special-purpose hardware are built
for solving hard instances of Quadratic Unconstrained Binary Optimization
(QUBO) problems. In terms of number of variables and precision of these
hardware are usually resource-constrained and they work either in Ising space
{-1,1} or in Boolean space {0,1}. Many naturally occurring problem instances
are higher-order in nature. The known method to reduce the degree of a
higher-order optimization problem uses Rosenberg's polynomial. The method works
in Boolean space by reducing the degree of one term by introducing one extra
variable. In this work, we prove that in Ising space the degree reduction of
one term requires the introduction of two variables. Our proposed method of
degree reduction works directly in Ising space, as opposed to converting an
Ising polynomial to Boolean space and applying previously known Rosenberg's
polynomial. For sparse higher-order Ising problems, this results in a more
compact representation of the resultant QUBO problem, which is crucial for
utilizing resource-constrained QUBO solvers.
