Hybrid Quantum-Classical Computing via Dantzig-Wolfe Decomposition for Integer Linear Programming

Numerous optimization scenarios such as industrial production planning, network communication routing, and logistic scheduling can be modeled as large-scale integer linear programming problems. However, due to the NP-Hardness of these problems, it is very challenging to optimally solve these problems in a short time on classical computers. Quantum computers have emerged as a new computing platform to provide new computing paradigms to tackle these problems. However, the scalability and efficiency of current quantum computers pose significant challenges in practical implementations of quantum optimization algorithms. In this paper, we propose a novel hybrid quantum-classical approach, termed Hybrid quantum-classical Dantzig-Wolfe Decomposition (HyDWD), aimed at solving these problems. In this framework, the subproblems can be solved in parallel on quantum computers. Our results demonstrate the benefits of integrating parallel quantum computing with the proposed hybrid quantum-classical framework via Dantzig-Wolfe decomposition, paving the way for advancements in optimization and decision-making processes.