Benchmarking the three-dimensional and the numerical three-dimensional matching problems on the D-Wave Advantage quantum annealer - Pandya, Komal; Maiti, Abyayananda (Information sciences, 2025)
This paper investigates the computational performance of the Three-Dimensional Matching (3DM) and the Numerical Three-Dimensional Matching (N3DM) problems on a quantum annealer. These problems have foundational significance in theoretical computer science and increasing relevance in real-world applications such as spatial crowdsourcing, task allocation, and resource scheduling. Motivated by the need to understand how emerging quantum hardware handles constrained combinatorial structures, we propose a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation for the 3DM problem, and adapt an existing formulation for N3DM. Both problems are implemented on D-Wave's Advantage System 4.1 quantum annealer using one-hot and domain wall constraint encoding schemes. We benchmark solver performance across multiple topological metrics, including physical qubit usage, embedding ratio, average chain length, and minimum Pegasus subgraph to embed the problem graph. For selected N3DM instances, we also consider Time-To-Solution (TTS) to gauge solver efficiency. To assess solution quality, we compare the quantum annealer's outputs against globally optimal solutions produced by the exact solvers such as Gurobi and CPLEX, as well as against high-quality approximations obtained via metaheuristics like Simulated Annealing (SA) and Tabu Search (TS). Hardware-oriented results from the quantum annealer indicate that the domain wall encoding consistently achieves more compact embeddings, shorter chains, and reduced hardware footprint, compared to one-hot encoding. Our findings on the optimality indicate that among classical solvers, Gurobi and CPLEX consistently return provably optimal solutions for both 3DM and N3DM, while SA and TS often produce high-quality solutions, particularly for small to medium-sized instances. The quantum annealer occasionally returns optimal solutions for 3DM instances. However, in the case of N3DM, the quality is generally inferior to classical methods, and no optimal solutions were returned by the quantum annealer across tested instances. This comparative study provides detailed insights into encoding efficiency, solver robustness, and quantum-classical trade-offs for solving computationally complex combinatorial optimization problems. •One-hot and domain wall encodings for 3DM and N3DM.•Domain wall encoding gives compact embeddings than one-hot.•Arithmetic constraints of N3DM impose more restrictions than 3DM.•Results obtained from the D-Wave quantum annealer are mostly suboptimal.•Comprehensive study of quantum-classical solution quality tradeoffs.