[Paper Review] Quantum and quantum-inspired optimization for solving the minimum bin packing problem

A. A. Bozhedarov, Aleksey S. Boev+4 more|arXiv (Cornell University)|Jan 26, 2023

Optimization and Packing Problems46 references4 citations

TL;DR

This paper formulates the spent nuclear fuel canister filling problem—critical for deep geological repositories—as a quadratic unconstrained binary optimization (QUBO) problem, enabling solution via quantum annealing and quantum-inspired algorithms. It demonstrates that while current quantum devices show promise for small-scale instances, quantum-inspired methods like the Simulated Bifurcation Machine outperform D-Wave for larger problems due to better scalability and lower time-to-solution.

ABSTRACT

Quantum computing devices are believed to be powerful in solving hard computational tasks, in particular, combinatorial optimization problems. In the present work, we consider a particular type of the minimum bin packing problem, which can be used for solving the problem of filling spent nuclear fuel in deep-repository canisters that is relevant for atomic energy industry. We first redefine the aforementioned problem it in terms of quadratic unconstrained binary optimization. Such a representation is natively compatible with existing quantum annealing devices as well as quantum-inspired algorithms. We then present the results of the numerical comparison of quantum and quantum-inspired methods. Results of our study indicate on the possibility to solve industry-relevant problems of atomic energy industry using quantum and quantum-inspired optimization.

Motivation & Objective

• Address the industrial challenge of optimizing spent nuclear fuel (SNF) loading into deep-repository canisters to minimize thermal output and maximize safety.
• Reframe the minimum bin packing problem for SNF management as a QUBO to enable use of quantum and quantum-inspired solvers.
• Benchmark quantum annealing (D-Wave) and quantum-inspired algorithms (Toshiba Simulated Bifurcation Machine) on problem instances of increasing size.
• Evaluate performance using time-to-solution (TTS) with 99% success probability to assess practical feasibility.
• Identify the limitations of current quantum hardware and the advantages of quantum-inspired alternatives for real-world nuclear energy applications.

Proposed method

• Formulate the spent nuclear fuel canister filling (CF) problem as a QUBO using binary variables to represent item-to-bin assignments.
• Encode constraints such as bin capacity and maximum fuel assemblies per canister into the QUBO matrix via penalty terms.
• Map the QUBO to the D-Wave 2000Q quantum annealer using a stable clique embedding and optimized chain strength.
• Implement the Simulated Bifurcation Machine (SBM) as a quantum-inspired classical algorithm to solve the same QUBO instances.
• Use time-to-solution (TTS) as the primary metric, calculated as TTS = t_a × R_99, where R_99 is the number of runs needed for 99% success probability.
• Fix annealing time at 20 μs (default) and run 10^4 repetitions per instance to ensure statistical reliability.

Experimental results

Research questions

• RQ1 Can the spent nuclear fuel canister filling problem be effectively encoded as a QUBO for quantum and quantum-inspired optimization?
• RQ2 How do quantum annealing (D-Wave) and quantum-inspired (SBM) methods compare in solving small- to medium-scale instances of the SNF packing problem?
• RQ3 What is the scalability of quantum and quantum-inspired approaches in terms of time-to-solution (TTS) as problem size increases?
• RQ4 What factors—such as energy gap, annealing time, or embedding quality—influence the success probability and solution quality on current quantum hardware?
• RQ5 To what extent can quantum-inspired algorithms outperform near-term quantum devices in practical nuclear energy applications?

Key findings

• The QUBO formulation successfully models the spent nuclear fuel canister filling problem with constraints on thermal power and fuel assembly limits.
• D-Wave quantum annealer achieves high success probability (27.7%) and low TTS (284 μs) for the smallest instance (2 elements), but fails to find optimal solutions for problems with 6 or more elements.
• Time-to-solution (TTS) increases significantly with problem size due to exponential growth in solution space and reduced success probability per run.
• Quantum-inspired Simulated Bifurcation Machine (SBM) shows superior scalability and lower TTS for larger problem instances compared to D-Wave, indicating practical advantages for real-world deployment.
• Increasing annealing time improves success probability but worsens TTS, so 20 μs was retained as the optimal default setting.
• Stable clique embedding with custom-optimized chain strength yields better solution stability than alternative embedding types, improving performance consistency.