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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| Veröffentlicht in: | Science China. Information sciences Jg. 65; H. 10; S. 200504 |
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Science China Press
01.10.2022
Springer Nature B.V |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| ArticleNumber | 200504 |
| Author | Li, Qingyu Huang, Yuhan Jin, Shan Wang, Xiaoting Hou, Xiaokai |
| Author_xml | – sequence: 1 givenname: Qingyu surname: Li fullname: Li, Qingyu organization: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China – sequence: 2 givenname: Yuhan surname: Huang fullname: Huang, Yuhan organization: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China – sequence: 3 givenname: Shan surname: Jin fullname: Jin, Shan organization: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China – sequence: 4 givenname: Xiaokai surname: Hou fullname: Hou, Xiaokai organization: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China – sequence: 5 givenname: Xiaoting surname: Wang fullname: Wang, Xiaoting email: xiaoting@uestc.edu.cn organization: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China |
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| Cites_doi | 10.1109/TSMCB.2008.925743 10.1145/1541880.1541882 10.1038/nphys3029 10.1103/PhysRevLett.113.210501 10.1007/BFb0055105 10.1038/nature23474 10.1007/s00220-006-0150-x 10.1103/PhysRevLett.113.130503 10.1145/331499.331504 10.1103/PhysRevLett.109.050505 10.1103/PhysRevA.103.042415 10.1007/s11222-007-9033-z 10.1103/PhysRevLett.103.220502 10.1007/s11432-019-2783-7 10.1103/PhysRevLett.100.160501 10.1145/1273496.1273497 10.1145/237814.237866 |
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| Keywords | Grover’s search quantum algorithm quantum phase estimation machine learning Hamiltonian simulation spectral clustering |
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| Snippet | 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... 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... |
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| SubjectTerms | 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 |
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