Papers › Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness
Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness
Nicola Franco, Tom Wollschläger, Benedikt Poggel, Stephan Günnemann, Jeanette Miriam Lorenz
Emerging quantum computing technologies, such as Noisy Intermediate-Scale Quantum (NISQ) devices, offer potential advancements in solving mathematical optimization problems. However, limitations in qubit availability, noise, and errors pose challenges for practical implementation. In this study, we examine two decomposition methods for Mixed-Integer Linear Programming (MILP) designed to reduce the original problem size and utilize available NISQ devices more efficiently. We concentrate on breaking down the original problem into smaller subproblems, which are then solved iteratively using a combined quantum-classical hardware approach. We conduct a detailed analysis for the decomposition of MILP with Benders and Dantzig-Wolfe methods. In our analysis, we show that the number of qubits required to solve Benders is exponentially large in the worst-case, while remains constant for Dantzig-Wolfe. Additionally, we leverage Dantzig-Wolfe decomposition on the use-case of certifying the robustness of ReLU networks. Our experimental results demonstrate that this approach can save up to 90\% of qubits compared to existing methods on quantum annealing and gate-based quantum computers.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections