On Quantum Computing for Mixed-Integer Programming: arXiv:2010.07852 [math.OC]

Quantum computing (QC) is emerging as a new computing resource that could be superior to conventional computing (CC) for certain classes of optimization problems. However, in principle QC can only solve unconstrained binary programming problems, while mixed-integer linear programming (MIP) is of most interest in practice. We attempt to bridge the gap between the capability of QC and real-world applications by developing a new approach for MIP. The idea is decomposing the MIP into binary programming and linear programming (LP) problems, which are respectively solved by QC and conventional computing. We formalize a decomposition approach that ensures that with a sufficient number of back and forth iterations, the algorithm can reach the optimal solution of the original MIP problem. The algorithm is tested on a 2000Q D-Wave quantum processing units (QPU) and is shown to be effective for small-scaled test cases.