<p>Quantum Annealing (QA) has gained attention as a promising approach for solving complex combinatorial optimization problems, relying on Quadratic Unconstrained Binary Optimization (QUBO) as its foundational framework. While QA offers potential advantages over classical methods, directly formulating problems within this paradigm often introduces scalability and embedding constraints, particularly on current quantum hardware with limited connectivity and qubit coherence. In this study, we examine the application of QA to the Bin Packing Problem (BPP), a well-known NP-hard challenge, and introduce preprocessing techniques to improve embedding feasibility. By strategically reducing redundancy through slack variable optimization and symmetry elimination, we achieve significant reductions in qubit consumption, chain lengths, and quadratic interactions, leading to more efficient embeddings. Experimental results on D-Wave’s Advantage System demonstrate that these optimizations broaden the range of problem instances that can be effectively processed, while also providing key insights into the challenges that remain for large-scale problem instances in current quantum architectures.</p>

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Optimizing bin packing problem on quantum annealers: A QUBO-based approach and scalability challenges

  • Samuel Deleplanque,
  • Amélia Durbec,
  • Amina El Yaagoubi

摘要

Quantum Annealing (QA) has gained attention as a promising approach for solving complex combinatorial optimization problems, relying on Quadratic Unconstrained Binary Optimization (QUBO) as its foundational framework. While QA offers potential advantages over classical methods, directly formulating problems within this paradigm often introduces scalability and embedding constraints, particularly on current quantum hardware with limited connectivity and qubit coherence. In this study, we examine the application of QA to the Bin Packing Problem (BPP), a well-known NP-hard challenge, and introduce preprocessing techniques to improve embedding feasibility. By strategically reducing redundancy through slack variable optimization and symmetry elimination, we achieve significant reductions in qubit consumption, chain lengths, and quadratic interactions, leading to more efficient embeddings. Experimental results on D-Wave’s Advantage System demonstrate that these optimizations broaden the range of problem instances that can be effectively processed, while also providing key insights into the challenges that remain for large-scale problem instances in current quantum architectures.