Towards solving industrial integer linear programs with decoded quantum interferometry

Abstract Optimization via decoded quantum interferometry (DQI) has recently gained a great deal of attention as a promising avenue for solving optimization problems using quantum computers. In this paper, we apply DQI to an industrial optimization problem in the automotive industry: the vehicle option-package pricing problem. Our main contributions are (1) formulating the industrial problem as an integer linear program (ILP), (2) converting the ILP into instances of max-XORSAT, and (3) developing a detailed quantum circuit implementation for belief propagation, a heuristic algorithm for decoding low density parity-check codes. Thus, we provide a full implementation of the DQI algorithm using Belief Propagation, which can be applied to any industrially relevant ILP by first transforming it into a max-XORSAT instance. We also evaluate the effectiveness of our implementation by benchmarking it against both Gurobi and a random sampling baseline.