Mixed-integer linear programming solver using Benders decomposition assisted by a neutral-atom quantum processor

This paper presents a hybrid classical-quantum approach to solve mixed-integer linear programming (MILP) using neutral-atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a subproblem, where the MP is addressed using a neutral-atom device, after being transformed into a quadratic unconstrained binary optimization (QUBO) model, with an automatized procedure. Our MILP to QUBO conversion tightens the upper bounds of the continuous variables involved, positively impacting the required qubit count, and the convergence of the algorithm. To solve the QUBO, we develop a heuristic for atom register embedding and apply a variational algorithm for pulse shaping. In addition, we implement a proof of concept that outperforms existing solutions. We also conduct preliminary numerical results: In a series of small MILP instances our algorithm identifies over 95% of feasible solutions of high quality, outperforming classical BD approaches where the MP is solved using simulated annealing.