aiqbench analysis
This research presents quantum algorithms that achieve polynomial speedups for density peak clustering, a core unsupervised learning task, by leveraging quantum Monte Carlo methods for density estimation. The study establishes theoretical advantages under specific scaling assumptions and provides numerical evidence suggesting these conditions hold for practically relevant datasets.
Quantum algorithms for four problems in density peak clustering
arXiv:2610.08498v1 Announce Type: new Abstract: Clustering is a fundamental task in unsupervised learning. The goal is to partition unlabeled data into clusters such that similar elements are assigned to the same cluster, while elements in different clusters are dissimilar. We propose a quantum Monte Carlo approach to density estimation, a key routine in density peak clustering. Building on this approach, we develop quantum algorithms for the full clustering problem and three related tasks: decision clustering, cluster counting, and heavy cluster counting. For each one, we establish a polynomial quantum query speedup under assumptions on the scaling of dataset-dependent parameters. Numerical experiments suggest that these conditions are satisfied for several practically relevant settings.
Abstract:Clustering is a fundamental task in unsupervised learning. The goal is to partition unlabeled data into clusters such that similar elements are assigned to the same cluster, while elements in different clusters are dissimilar. We propose a quantum Monte Carlo approach to density estimation, a key routine in density peak clustering. Building on this approach, we develop quantum algorithms for the full clustering problem and three related tasks: decision clustering, cluster counting, and heavy cluster counting. For each one, we establish a polynomial quantum query speedup under assumptions on the scaling of dataset-dependent parameters. Numerical experiments suggest that these conditions are satisfied for several practically relevant settings.
arXiv:2610.08498 [quant-ph]
(or arXiv:2610.08498v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.08498 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 198 words
