Research on error-correcting codes that make quantum information technology stubborn

2008 Fiscal Year Final Research Report

• Project/Area Number: 18700017
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Fundamental theory of informatics
• Research Institution: National Institute of Advanced Industrial Science and Technology
• Principal Investigator: HAGIWARA Manabu National Institute of Advanced Industrial Science and Technology, 情報セキュリティ研究センター, 研究員 (80415728)
• Project Period (FY): 2006 – 2009
• Keywords: 量子誤り訂正符号 / CSS符号 / LDPC符号 / 組合せ論

Research Abstract

CSS符号(量子誤り訂正符号)を構成する古典符号の対をQC-LDPC符号として実現する手法を提案した。QC-LDPC符号を特徴づけるモデル行列による、CSS符号構成の必要十分条件を簡潔に与え、さらにその条件を満たす、具体的な構成方法を提示した。その発展として、QC-LDPC符号の組がCSS符号を構成する為の符号長とモデル行列構成要素である巡回行列のサイズに関する下限導出に成功した。また、量子誤り訂正シミュレータを古典計算機上で開発した。

Research Products

• [Journal Article] Comment on "Quasi-Cyclic Low Density Parity Check Codes from Circulant Permutation Matrix" (2009)
  • Author(s): Manabu Hagiwara, Marc Fossorier
  • Journal Title: IEEE Transactions on Information Theory vol.55-3 Pages: 1430-1430
  • Peer Reviewed
• [Journal Article] Error-Correcting Codes and Cryptography (2008)
  • Author(s): Hideki Imai, Manabu Hagiwara
  • Journal Title: Applicable Algebra In Engineering Communication and Computing vol.19-3 Pages: 213-228
  • Peer Reviewed
• [Journal Article] A Simple Construction of Quantum Quasi-Cyclic LDPC Codes (2007)
  • Author(s): Manabu Hagiwara, Hidaki Imai
  • Journal Title: Proc. Of 2007 Hawaii and SITA Joint Conference on Information Theory vol.1 Pages: 19-23
  • Peer Reviewed
• [Journal Article] On Minimal Length of Quasi Cyclic LDPC Codes with Girth Greater Than or Equal to 6 (2006)
  • Author(s): Manabu Hagiwara, Koji Nuida, Takashi Kitagawa, Marc Fossorier, Hideki Imai
  • Journal Title: Proc. Of The 2006 International Symposium on Information Theory and its Applications vol.1 Pages: (CD-ROM)
  • Peer Reviewed
• [Journal Article] On a Construction of a Non-stabilizer Clifford Quantum Code for 2h(2j+1)-Level States (2006)
  • Author(s): Manabu Hagiwara, Hideki Imai
  • Journal Title: Electronics and Communications in Japan Part III-Fundamental Electronic Science Apr-90 Pages: 63-68
  • Peer Reviewed
• [Presentation] 準巡回低密度パリティ検査符号にまつわる離散数学的側面と量子符号への拡張にまつわる問題 (2008)
  • Author(s): 萩原学
  • Organizer: COS 08
  • Place of Presentation: 沖縄県
  • Year and Date: 2008-09-09
• [Presentation] ねじれ関係にあるLDPC符号の組の構成 (2007)
  • Author(s): 萩原学, 今井秀樹
  • Organizer: 情報理論とその応用シンポジウム
  • Place of Presentation: 三重県
  • Year and Date: 2007-11-27
• [Presentation] Quantum Error-Correcting Codes (2007)
  • Author(s): Manabu Hagiwara
  • Organizer: Summer School on Mathematical Aspects of Quantum Computing
  • Place of Presentation: Kinki University
  • Year and Date: 2007-08-27
• [Presentation] Quantum Quasi-Cyclic LDPC Codes (2007)
  • Author(s): Manabu Hagiwara, Hideki Imai
  • Organizer: 2007 IEEE International Symposium on Information Theory
  • Place of Presentation: Nice
  • Year and Date: 2007-06-26
• [Presentation] 非正則疑似巡回低密度パリティ検査符号の量子符号化にまつわる組合せ論的アプローチ
  • Author(s): 萩原学
• [Remarks] 研究成果ホームページ
  • URL: http://staff.aist.go.jp/hagiwara.hagiwara/qecc/qecc.html