  In this work, we attempt to solve the integer-weight knapsack problem using
the D-Wave 2000Q adiabatic quantum computer. The knapsack problem is a
well-known NP-complete problem in computer science, with applications in
economics, business, finance, etc. We attempt to solve a number of small
knapsack problems whose optimal solutions are known; we find that adiabatic
quantum optimization fails to produce solutions corresponding to optimal
filling of the knapsack in all problem instances. We compare results obtained
on the quantum hardware to the classical simulated annealing algorithm and two
solvers employing a hybrid branch-and-bound algorithm. The simulated annealing
algorithm also fails to produce the optimal filling of the knapsack, though
solutions obtained by simulated and quantum annealing are no more similar to
each other than to the correct solution. We discuss potential causes for this
observed failure of adiabatic quantum optimization.
