A clustering aggregation algorithm on neutral-atoms and annealing quantum processors

TL;DR

This work tackles clustering aggregation, a robust consensus approach for combining multiple clusterings, by casting it as a Maximum-Weight Independent Set (MWIS) and then as a QUBO problem suitable for quantum annealers. The authors propose a hybrid quantum-classical pipeline that builds an overlap graph from multiple clusterings, uses silhouette-based weights, and solves either MIS or MWIS on Pasqal's neutral-atom Fresnel (MIS-capable in analog mode) or D-Wave's Advantage (QUBO with constraints). Empirical evaluation on small and large datasets shows partial feasibility: real hardware and emulators sometimes recover the correct cluster counts, but no quantum advantage is yet demonstrated, with performance highly platform-dependent. The study highlights the potential of cross-technology benchmarking and hybrid pipelines while outlining practical limitations and directions for improvement, including future gate-based approaches and enhanced problem encodings.

Abstract

This work presents a hybrid quantum-classical algorithm to perform clustering aggregation, designed for neutral-atoms quantum computers and quantum annealers. Clustering aggregation is a technique that mitigates the weaknesses of clustering algorithms, an important class of data science methods for partitioning datasets, and is widely employed in many real-world applications. By expressing the clustering aggregation problem instances as a Maximum Independent Set (MIS) problem and as a Quadratic Unconstrained Binary Optimization (QUBO) problem, it was possible to solve them by leveraging the potential of Pasqal's Fresnel (neutral-atoms processor) and D-Wave's Advantage QPU (quantum annealer). Additionally, the designed clustering aggregation algorithm was first validated on a Fresnel emulator based on QuTiP and later on an emulator of the same machine based on tensor networks, provided by Pasqal. The results revealed technical limitations, such as the difficulty of adding additional constraints on the employed neutral-atoms platform and the need for better metrics to measure the quality of the produced clusterings. However, this work represents a step towards a benchmark to compare two different machines: a quantum annealer and a neutral-atom quantum computer. Moreover, findings suggest promising potential for future advancements in hybrid quantum-classical pipelines, although further improvements are needed in both quantum and classical components.

Figures (14)

• Figure 1: Steps of the proposed algorithm.
• Figure 2: Example dataset, generated with function make_blobs from module sklearn.dataset, containing 300 points divided in three blobs.
• Figure 3: Three clusterings of the original dataset, all of which obtained via K-Means with number of clusters equal to 2 and seed chosen in order to obtain different results. (a) contains clusters with labels 0 and 1; (b) contains clusters with labels 2 and 3; (c) contains clusters with labels 4 and 5.
• Figure 4: Adjacency graph for the example dataset.
• Figure 5: Plot of the dataset used to test the hybrid clustering aggregation algorithm, made up of 788 points. The different colors indicate the 7 clusters of the clustering considered optimal.