Performance of Commercial Quantum Annealing Solvers for the Capacitated Vehicle Routing Problem

Abstract: Quantum annealing (QA) is a heuristic search algorithm that can run on Adiabatic Quantum Computation (AQC) processors to solve combinatorial optimization problems. Although theoretical studies and simulations on classic hardware have shown encouraging results, these analyses often assume that the computation occurs in adiabatically closed systems without environmental interference. This is not a realistic assumption for real systems; therefore, without extensive empirical measurements on real quantum platforms, theory-based predictions, simulations on classical hardware or limited tests do not accurately assess the current commercial capabilities. This study has assessed the quality of the solution provided by a commercial quantum annealing platform compared to known solutions for the Capacitated Vehicle Routing Problem (CVRP). The study has conducted extensive analysis over more than 30 hours of access to QA commercial platforms to investigate how the size of the problem and its complexity impact the solution accuracy and the time used to find a solution. Our results have found that the absolute error is between 0.12 and 0.55, and the quantum processor unit (QPU) time is between 30 and 46 micro seconds. Our results show that as the constraint density increases, the quality of the solution degrades. Therefore, more than the problem size, the model complexity plays a critical role, and practical applications should select formulations that minimize the constraint density.