Abstract:
In this paper, we present e cient quadratic unconstrained binary optimization (QUBO) formulations for the mixed dominating set and the weighted mixed dominating set problems, which are both NP-hard. By using a D-Wave 2X quantum computer with 1098 active qubits, the QUBO formulation of the unweighted mixed dominating
set is tested on several small graphs. In every test graph, 30K samples were taken on the D-Wave computer in two di erent execution modes (with and without post-processing optimization). The experimental results achieved optimal answers in the majority of the cases. The correctness of the formulations are proven, establishing empirical evidence that our formulation and their implementations are correct.