Hybrid quantum-classical unsupervised data clustering based on the self-organizing feature map

Physical Review A: Atomic, Molecular, and Optical physics. 2025. Vol. 111. No. 012416. Article 012416.

Lazarev I., Narozniak M., Byrnes T., Pyrkov A. N.

Unsupervised machine learning is one of the main techniques employed in artificial intelligence. We introduce an algorithm for quantum-assisted unsupervised data clustering using the self-organizing feature map, a type of artificial neural network. The complexity of our algorithm scales as 𝑂⁡(𝐿⁢𝑁), in comparison to the classical case which scales as 𝑂⁡(𝐿⁢𝑀⁢𝑁), where 𝑁 is the number of samples, 𝑀 is the number of randomly sampled cluster vectors, and 𝐿 is the number of the shifts of cluster vectors. We perform a proof-of-concept demonstration of one of the central components on the IBM quantum computer and show that it allows us to reduce the number of calculations in the number of clusters. Our algorithm exhibits exponential decrease in the errors of the distance matrix with the number of runs of the algorithm.

Keywords: quantum algorithms, Machine Learning, quantum circuits