  Quantum computing is emerging as a new computing resource that could be
superior to conventional computing for certain classes of optimization
problems. However, in principle, most existing approaches to quantum
optimization are intended to solve unconstrained binary programming problems,
while mixed-integer linear programming is of most interest in practice. We
attempt to bridge the gap between the capability of quantum computing and
real-world applications by developing a new approach for mixed-integer
programming. The approach applies Benders decomposition to decompose the
mixed-integer programming into binary programming and linear programming
sub-problems, which are solved by a noisy intermediate-scale quantum processor
and conventional processor, respectively. The algorithm is provably able to
reach the optimal solution of the original mixed-integer programming problem.
The algorithm is tested on a D-Wave 2000Q quantum processing unit and is shown
to be effective for small-scaled test cases. We also test the algorithm on a
mixed-integer programming inspired by power system applications. Many insights
are drawn from the numerical results for both the capabilities and limitations
of the proposed algorithm.
