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The Quantum Approximate Optimization Algorithm (QAOA) has been one of theleading candidates for near-term quantum advantage in gate-model quantumcomputers. From its inception, this algorithm has sparked the desire forcomparison between gate-model and annealing platforms. When preparing problemstatements for these algorithms, the predominant inclination has been toformulate a quadratic Hamiltonian. This paper gives an example of a graphcoloring problem that, depending on its variable encoding scheme, optionallyadmits higher order terms. This paper presents evidence that the higher orderformulation is preferable to two other encoding schemes. The evidence thenmotivates an analysis of the scaling behavior of QAOA in this higher orderformulation for an ensemble of graph coloring problems.

QAOA of the Highest Order