  Here we consider using quantum annealing to solve Set Cover with Pairs (SCP),
an NP-hard combinatorial optimization problem that play an important role in
networking, computational biology, and biochemistry. We show an explicit
construction of Ising Hamiltonians whose ground states encode the solution of
SCP instances. We numerically simulate the time-dependent Schr\"{o}dinger
equation in order to test the performance of quantum annealing for random
instances and compare with that of simulated annealing. We also discuss
explicit embedding strategies for realizing our Hamiltonian construction on the
D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding
on the Chimera graph preserves the structure of the original SCP instance and
in particular, the embedding for general complete bipartite graphs and logical
disjunctions may be of broader use than that the specific problem we deal with.
