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Paper Abstract and Keywords
Presentation 2021-11-30 10:30
Quantum computational approach for topological data analysis -- Quantum algorithm for persistent Betti numbers --
Ryu Hayakawa (Kyoto Univ.)
Abstract (in Japanese) (See Japanese page) 
(in English) Topological data analysis (TDA) based on persistent homology is an emergent field of data analysis. The critical step of TDA is computing the persistent Betti numbers. Existing classical algorithms for TDA have been limited because the number of simplices can grow exponentially in the size of data for high-dimensional analysis. In the context of quantum computation, it has been previously shown that there exists an efficient quantum algorithm for estimating the Betti numbers even in high dimensions. However, the Betti numbers are less general than the persistent Betti numbers, and there have been no quantum algorithms that can estimate the persistent Betti numbers of arbitrary dimensions. This paper shows the first quantum algorithm that can estimate the persistent Betti numbers of arbitrary dimensions. Our algorithm is efficient for the construction of simplicial complexes such as the Vietoris-Rips complex and demonstrates exponential speedup over the known classical algorithms.
Keyword (in Japanese) (See Japanese page) 
(in English) Quantum computing / quantum algorithm / TDA / Persistent Homology / / / /  
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Conference Information
Committee QIT  
Conference Date 2021-11-30 - 2021-12-01 
Place (in Japanese) (See Japanese page) 
Place (in English) Online 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Quantum Information 
Paper Information
Registration To QIT 
Conference Code 2021-11-QIT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Quantum computational approach for topological data analysis 
Sub Title (in English) Quantum algorithm for persistent Betti numbers 
Keyword(1) Quantum computing  
Keyword(2) quantum algorithm  
Keyword(3) TDA  
Keyword(4) Persistent Homology  
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1st Author's Name Ryu Hayakawa  
1st Author's Affiliation Kyoto University (Kyoto Univ.)
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Speaker Author-1 
Date Time 2021-11-30 10:30:00 
Presentation Time 20 minutes 
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