HYBRID QUANTUM-CLASSICAL ALGORITHMS IN LOGISTICS OPTIMIZATION PROBLEMS

The paper considers the application of hybrid quantum-classical algorithms (HQCA) to optimization problems in logistics, such as the vehicle routing problem (VRP), the traveling salesman problem (TSP), as well as their generalizations with time windows and fleet constraints. A multi-level architecture of hybrid computing is presented, including the stages of problem translation into QUBO form, implementation of variational quantum algorithms (QAOA), annealing on quantum systems (e.g., D-Wave Advantage2), as well as methods for error correction and post-processing of solutions. A review of domestic and foreign developments in this area is conducted, including the results of Russian research groups (RKC, MISiS, Innopolis, MIPT). It is experimentally shown that GCQAs provide gains in quality and time for medium-sized tasks (100–1 clients), especially when using warm-start strategies and dynamic load distribution between classical and quantum subsystems. The limitations of current NISQ devices and scaling prospects, including integration with predictive analytics and digital twins of logistics systems, are discussed.