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arXiv:0905.3527

Quantum Annealing for Clustering

Kenichi Kurihara, Shu Tanaka, Seiji Miyashita

Published May 21, 2009• 9 citations
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Abstract

This paper studies quantum annealing (QA) for clustering, which can be seen as an extension of simulated annealing (SA). We derive a QA algorithm for clustering and propose an annealing schedule, which is crucial in practice. Experiments show the proposed QA algorithm finds better clustering assignments than SA. Furthermore, QA is as easy as SA to implement.

DOI
10.48550/arxiv.0905.3527

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This paper studies quantum annealing (QA) for clustering, which can be seen as an extension of simulated annealing (SA). We derive a QA algorithm for clustering and propose an annealing schedule, which is crucial in practice. Experiments show the proposed QA algorithm finds better clustering assignments than SA. Furthermore, QA is as easy as SA to implement.
This paper explores the applications of quantum annealing (QA) and classical simulated annealing (SA) to a suite of combinatorial optimization problems in machine learning, namely feature selection, instance selection, and clustering. We formulate each task as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement both quantum and classical solvers to compare their effectiveness. For feature selection, we propose several QUBO configurations that balance feature importance and redundancy, showing that quantum annealing (QA) produces solutions that are computationally more efficient. In instance selection, we propose a few novel heuristics for instance-level importance measures that extend existing methods. For clustering, we embed a classical-to-quantum pipeline, using classical clustering followed by QUBO-based medoid refinement, and demonstrate consistent improvements in cluster compactness and retrieval metrics. Our results suggest that QA can be a competitive and efficient tool for discrete machine learning optimization, even within the constraints of current quantum hardware.
Quantum annealing (QA) algorithm is a new quantum optimization algorithm based on the classical simulated annealing (SA) algorithm. Unlike classical SA algorithm, which uses the thermal waves to search for the optimal solution, the QA algorithm uses the quantum tunneling effect to allow a quantum to penetrate a potential barrier with a higher energy than itself. Therefore, the algorithm can get rid of the local extreme values and is more likely to approach the global optimal with higher probability. In the literature, the QA algorithm has shown perfect optimization effects on combinatorial optimization problems. In this paper, the basic concepts and application fields of QA algorithm, which is the core principle of D-Wave quantum computer, are systematically reviewed. The applications of QA algorithm in cryptography, traveling salesman problem, graph coloring problem, and traffic path are discussed in detail. In addition, the direction of future research for QA algorithm is explored.