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Paper Abstract and Keywords
Presentation 2021-05-24 10:10
Quantum-Classical Hybrid Algorithm for LWE Problems
Yasuhito Kawano (Chubu Univ.)
Abstract (in Japanese) (See Japanese page) 
(in English) This paper introduces a quantum-inspired algorithm, called interpolation, that reduces an LWE problem to another problem similar to an LWE problem (called an LWE-like problem in this paper). The interpolation algorithm can change a modulus of an LWE problem, which makes it easier to solve an LWE problem by a quantum (or quantum-inspired) computer. In addition, we propose a quantum-classical hybrid algorithm that solves an LWE problem by using the interpolation algorithm and a quantum annealing machine recursively. The sizes of graphs of maximum independent set (MIS) problems reduced from an LWE problem are calculated. The number of qubits necessary to solve an LWE problem by using a quantum annealing machine is then estimated. For example, a 40-dimensional LWE problem, which is the smallest-dimensional open problem of Darmstadt LWE Challenge, can be reduced to MIS problems of graphs with about several tens of thousands of vertices and small weights. This suggests that open problems of Darmstadt LWE Challenge will be in the scope of the target of quantum annealing machines in the near future.
We implemented the interpolation algorithm and confirmed that the smallest challenge problem (dimension $=40$ and relative error $=0.05$) of Darmstadt LWE Challenge
can be reduced to a graph with about 40,000 vertices.
Keyword (in Japanese) (See Japanese page) 
(in English) Quantum Computer / Quantum Algorithm / Quantum-Classical Hybrid Algorithm / LWE Cryptography / Post-Quantum Cryptography / Challenge Problem / Quantum Annealing Machine /  
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Conference Information
Committee QIT  
Conference Date 2021-05-24 - 2021-05-25 
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 2021-05-QIT 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Quantum-Classical Hybrid Algorithm for LWE Problems 
Sub Title (in English)  
Keyword(1) Quantum Computer  
Keyword(2) Quantum Algorithm  
Keyword(3) Quantum-Classical Hybrid Algorithm  
Keyword(4) LWE Cryptography  
Keyword(5) Post-Quantum Cryptography  
Keyword(6) Challenge Problem  
Keyword(7) Quantum Annealing Machine  
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1st Author's Name Yasuhito Kawano  
1st Author's Affiliation Chubu University (Chubu Univ.)
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Speaker Author-1 
Date Time 2021-05-24 10:10:00 
Presentation Time 20 minutes 
Registration for QIT 
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