  Quantum annealing is a promising heuristic method to solve combinatorial
optimization problems, and efforts to quantify performance on real-world
problems provide insights into how this approach may be best used in practice.
We investigate the empirical performance of quantum annealing to solve the
Nurse Scheduling Problem (NSP) with hard constraints using the D-Wave 2000Q
quantum annealing device. NSP seeks the optimal assignment for a set of nurses
to shifts under an accompanying set of constraints on schedule and personnel.
After reducing NSP to a novel Ising-type Hamiltonian, we evaluate the solution
quality obtained from the D-Wave 2000Q against the constraint requirements as
well as the diversity of solutions. For the test problems explored here, our
results indicate that quantum annealing recovers satisfying solutions for NSP
and suggests the heuristic method is sufficient for practical use. Moreover, we
observe that solution quality can be greatly improved through the use of
reverse annealing, in which it is possible to refine a returned results by
using the annealing process a second time. We compare the performance NSP using
both forward and reverse annealing methods and describe how these approach
might be used in practice.
