  We report on a case study in programming an early quantum annealer to attack
optimization problems related to operational planning. While a number of
studies have looked at the performance of quantum annealers on problems native
to their architecture, and others have examined performance of select problems
stemming from an application area, ours is one of the first studies of a
quantum annealer's performance on parametrized families of hard problems from a
practical domain. We explore two different general mappings of planning
problems to quadratic unconstrained binary optimization (QUBO) problems, and
apply them to two parametrized families of planning problems, navigation-type
and scheduling-type. We also examine two more compact, but problem-type
specific, mappings to QUBO, one for the navigation-type planning problems and
one for the scheduling-type planning problems. We study embedding properties
and parameter setting, and examine their effect on the efficiency with which
the quantum annealer solves these problems. From these results we derive
insights useful for the programming and design of future quantum annealers:
problem choice, the mapping used, the properties of the embedding, and the
annealing profile all matter, each significantly affecting the performance.
