Quantum spectral clustering algorithm for unsupervised learning

Clustering is one of the most crucial problems in unsupervised learning, and the well-known k -means algorithm can be implemented on a quantum computer with a significant speedup. However, for the clustering problems that cannot be solved using the k -means algorithm, a powerful method called spectr...

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Bibliographic Details
Published in:Science China. Information sciences Vol. 65; no. 10; p. 200504
Main Authors: Li, Qingyu, Huang, Yuhan, Jin, Shan, Hou, Xiaokai, Wang, Xiaoting
Format: Journal Article
Language:English
Published: Beijing Science China Press 01.10.2022
Springer Nature B.V
Subjects:
Algorithms
Circuit design
Clustering
Computer Science
Datasets
Design
Eigenvalues
Eigenvectors
Entangled states
Information Systems and Communication Service
Interdisciplinary subjects
Machine learning
Microprocessors
Quantum computers
Quantum computing
Quantum entanglement
Random access memory
Research Paper
Science
Unsupervised learning
Grover’s search
quantum algorithm
quantum phase estimation
machine learning
Hamiltonian simulation
spectral clustering
ISSN:1674-733X, 1869-1919
Online Access:Get full text
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Summary:Clustering is one of the most crucial problems in unsupervised learning, and the well-known k -means algorithm can be implemented on a quantum computer with a significant speedup. However, for the clustering problems that cannot be solved using the k -means algorithm, a powerful method called spectral clustering is used. In this study, we propose a circuit design to implement spectral clustering on a quantum processor with substantial speedup by initializing the processor into a maximally entangled state and encoding the data information into an efficiently simulatable Hamiltonian. Compared to the established quantum k -means algorithms, our method does not require a quantum random access memory or a quantum adiabatic process. It relies on an appropriate embedding of quantum phase estimation into Grover’s search to gain the quantum speedup. Simulations demonstrate that our method effectively solves clustering problems and is an important supplement to quantum k -means algorithm for unsupervised learning.
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ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-022-3492-x