  Today, hardware constraints are an important limitation on quantum adiabatic
optimization algorithms. Firstly, computational problems must be formulated as
quadratic unconstrained binary optimization (QUBO) in the presence of noisy
coupling constants. Secondly, the interaction graph of the QUBO must have an
effective minor embedding into a two-dimensional nonplanar lattice graph. We
describe new strategies for constructing QUBOs for NP-complete/hard
combinatorial problems that address both of these challenges. Our results
include asymptotically improved embeddings for number partitioning, filling
knapsacks, graph coloring, and finding Hamiltonian cycles. These embeddings can
be also be found with reduced computational effort. Our new embedding for
number partitioning may be more effective on next-generation hardware.
