Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness

Nicola Franco, Tom Wollschläger, Benedikt Poggel, Stephan Günnemann, Jeanette Miriam Lorenz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationProceedings - 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023
EditorsHausi Muller, Yuri Alexev, Andrea Delgado, Greg Byrd
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages524-534
Number of pages11
ISBN (Electronic)9798350343236
DOIs
StatePublished - 2023
Event4th IEEE International Conference on Quantum Computing and Engineering, QCE 2023 - Bellevue, United States
Duration: 17 Sep 202322 Sep 2023

Publication series

NameProceedings - 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023
Volume1

Conference

Conference4th IEEE International Conference on Quantum Computing and Engineering, QCE 2023
Country/TerritoryUnited States
CityBellevue
Period17/09/2322/09/23

Keywords

  • Hybrid Algorithm
  • Mixed-Integer Linear Programming
  • Quantum Computing

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