Quantum Annealing for Combinatorial Optimization: A Benchmarking Study

2025-04-08

AI Summary

This work addresses the critical open question of whether quantum annealing delivers practical quantum advantage for combinatorial optimization. For the first time, it systematically evaluates performance on large-scale, dense Hamiltonian instances (50 in total) using a 5000+-qubit superconducting quantum annealer. We propose a hybrid solver framework integrating problem-specific minor embedding, chain correction, and classical preprocessing, enabling end-to-end validation on physical hardware. Results demonstrate a statistically significant quantum advantage: the quantum approach achieves a 0.013% improvement in solution accuracy and a 6,561× speedup over state-of-the-art classical solvers. This constitutes the first empirical evidence of simultaneous high-precision and ultra-fast quantum advantage on large-scale optimization problems. Crucially, the results highlight the transformative potential of quantum-classical co-design—where tailored quantum hardware integration with classical pre- and post-processing unlocks performance beyond either paradigm alone.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements

Abstract

Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5,000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6,561x) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.

Problem

• Evaluating quantum annealing's performance vs classical solvers
• Solving large dense Hamiltonian optimization problems efficiently
• Achieving higher accuracy and speed with quantum annealing

Innovation

• Quantum annealing with 5,000+ qubits
• Hybrid architecture enhances performance
• State-of-the-art quantum solver benchmarks