Quantum Fourier Transform over Non-Abelian Groups and Its Application

2015 Fiscal Year Final Research Report

• Project/Area Number: 25330021
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: NTT Communication Science Laboratories
• Principal Investigator: Kawano Yasuhito 日本電信電話株式会社NTTコミュニケーション科学基礎研究所, メディア情報研究部, 主任研究員 (40396180)
• Co-Investigator(Kenkyū-buntansha): 関川 浩 東京理科大学, 理学部, 教授 (00396178)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 量子コンピュータ / 量子アルゴリズム / 量子フーリエ変換 / 量子暗号 / ポスト量子暗号 / 格子暗号 / 非可換群 / 表現論

Outline of Final Research Achievements

A quantum computer, which is expected to be the next generation machine, achieves high-performance computing using superpositions of qubits. Its performance depends on the quantum algorithms. The study of quantum algorithms is then necessary for practical applications of quantum computers. We proposed the fastest quantum Fourier transform over non-abelian groups at this moment. In addition, we proposed a new quantum algorithm that solves lattice problems by generalizing a known algorithm that factors large composite integers. Our result can be applied to the studies of artificial intelligence and the next-generation post-quantum public-key cryptography.

Free Research Field

量子情報科学