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Quadratic unconstrained binary optimization (QUBO) can be seen as a genericlanguage for optimization problems. QUBOs attract particular attention sincethey can be solved with quantum hardware, like quantum annealers or quantumgate computers running QAOA. In this paper, we present two novel QUBOformulations for $k$-SAT and Hamiltonian Cycles that scale significantly betterthan existing approaches. For $k$-SAT we reduce the growth of the QUBO matrixfrom $O(k)$ to $O(log(k))$. For Hamiltonian Cycles the matrix no longer growsquadratically in the number of nodes, as currently, but linearly in the numberof edges and logarithmically in the number of nodes.  We present these two formulations not as mathematical expressions, as mostQUBO formulations are, but as meta-algorithms that facilitate the design ofmore complex QUBO formulations and allow easy reuse in larger and more complexQUBO formulations.

Algorithmic QUBO Formulations for k-SAT and Hamiltonian Cycles