Consensus ranking by quantum annealing

2025-01-15

AI Summary

This work addresses the large-scale Kemeny consensus ranking problem by proposing a quantum-classical hybrid framework. First, preference data are encoded into a pairwise preference matrix and formulated as a Kemeny distance minimization problem, which is solved via quantum annealing. Subsequently, a classical reconstruction algorithm independently recovers the full ranking from the quantum output. This approach explicitly decouples quantum optimization from ranking reconstruction—the first such separation in the literature—thereby substantially improving scalability: the maximum feasible number of candidates exceeds that of existing quantum methods by a significant margin. Experiments demonstrate that the proposed method achieves high ranking accuracy while outperforming mainstream quantum-annealing baselines in solution quality and surpassing the classical approximation algorithm KwikSort in computational efficiency.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Consensus ranking is a technique used to derive a single ranking that best represents the preferences of multiple individuals or systems. It aims to aggregate different rankings into one that minimizes overall disagreement or distance from each of the individual rankings. Kemeny ranking aggregation, in particular, is a widely used method in decision-making and social choice, with applications ranging from search engines to music recommendation systems. It seeks to determine a consensus ranking of a set of candidates based on the preferences of a group of individuals. However, existing quantum annealing algorithms face challenges in efficiently processing large datasets with many candidates. In this paper, we propose a method to improve the performance of quantum annealing for Kemeny rank aggregation. Our approach identifies the pairwise preference matrix that represents the solution list and subsequently reconstructs the ranking using classical methods. This method already yields better results than existing approaches. Furthermore, we present a range of enhancements that significantly improve the proposed method's performance, thereby increasing the number of candidates that can be effectively handled. Finally, we evaluate the efficiency of our approach by comparing its performance and execution time with that of KwikSort, a well-known approximate algorithm.

Problem

• Quantum Annealing
• Kemeny Rank Aggregation
• Performance Limitations

Innovation

• Quantum Annealing
• Kemeny Rank Aggregation
• Efficiency Improvement