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Paper Abstract and Keywords
Presentation 2014-05-12 00:00
[Poster Presentation] statistical mechanics formulation of prime factorization
Chihiro H Nakajima (Tohoku Univ.)
Abstract (in Japanese) (See Japanese page) 
(in English) We propose a new approach to solve the problem of the prime factorization, formulating the problem as a ground state searching problem of statistical mechanics Hamiltonian. This formulation is expected to give a new insight to this problem. Especially in the context of computational complexity, one would expect to yield the information which leads to determination of the typical case computational complexity of the factorizing process. With this perspective, first we perform simulation with replica exchange Monte Carlo method. We investigated the first passage time that the correct form of prime factorization is found and observed the behavior which seems to indicate exponential computational hardness.
The above result is followed by the analysis of the density of states on two macroscopic quantities; energy and hamming distence from correct solutions. The behavior of the density of states seems to imply the complex energy landscape with many local minima.
Keyword (in Japanese) (See Japanese page) 
(in English) replica exchange Monte Carlo mathod / prime factorization / statistical mechanics / / / / /  
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Conference Information
Committee QIT  
Conference Date 2014-05-12 - 2014-05-13 
Place (in Japanese) (See Japanese page) 
Place (in English) Nagoya Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Quantum Information 
Paper Information
Registration To QIT 
Conference Code 2014-05-QIT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) statistical mechanics formulation of prime factorization 
Sub Title (in English)  
Keyword(1) replica exchange Monte Carlo mathod  
Keyword(2) prime factorization  
Keyword(3) statistical mechanics  
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1st Author's Name Chihiro H Nakajima  
1st Author's Affiliation Tohoku University (Tohoku Univ.)
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Date Time 2014-05-12 00:00:00 
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