  We are interested in benchmarking both quantum annealing and classical
algorithms for minimizing Quadratic Unconstrained Binary Optimization (QUBO)
problems. Such problems are NP-hard in general, implying that the exact minima
of randomly generated instances are hard to find and thus typically unknown.
While brute forcing smaller instances is possible, such instances are typically
not interesting due to being too easy for both quantum and classical
algorithms. In this contribution, we propose a novel method, called posiform
planting, for generating random QUBO instances of arbitrary size with known
optimal solutions, and use those instances to benchmark the sampling quality of
four D-Wave quantum annealers utilizing different interconnection structures
(Chimera, Pegasus, and Zephyr hardware graphs) as well as the simulated
annealing algorithm. Posiform planting differs from many existing methods in
two key ways. It ensures the uniqueness of the planted optimal solution, thus
avoiding groundstate degeneracy, and it enables the generation of QUBOs that
are tailored to a given hardware connectivity structure, provided that the
connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT
boolean satisfiability combinatorial optimization problems. Our experiments
demonstrate the capability of the D-Wave quantum annealers to sample the
optimal planted solution of combinatorial optimization problems with up to
$5627$ qubits.
