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

• 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
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,240,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 量子誤り訂正符号 / CSS符号 / LDPC符号 / 組合せ論 / 低密度パリティ検査符号 / 量子LDPC符号 / 疑似巡回符号 / 疑似巡回LDPC符号 / 擬似巡回LDPC符号

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] 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 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] Error-Correcting Codes and Cryptography (2008)
  • Author(s): Hidaki IMAI, Manabu Hagiwara
  • Journal Title: Applicable Algebra In Engineering Communication and Computing 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] A Simple Construction of Quantum Quasi-Cyclic LDPC codes (2007)
  • Author(s): Manabu Hagiwara, Hideki Imai
  • Journal Title: 2007 Hawaii and SITA Joint Conference on Information Theory (HISC) 1 Pages: 19-23
• [Journal Article] Quantum Quasi-Cyclic LDPC codes (2007)
  • Author(s): Manabu Hagiwara, Hideki Imai
  • Journal Title: Proceeding of 2007 IEEE International Symposium on Information Theory (ISIT2007) 1 Pages: 806-810
  • Peer Reviewed
• [Journal Article] A Quantum Secure Direct Communication Protocol for Sending A Quantum State and Its Security Analysis (2007)
  • Author(s): Yumiko Murakami, Masaki Nakanisbi, Manabu Hagiwara, Shigeru Yamashita, Yasuhiko Nakashima
  • Journal Title: Proceeding of The 6th WSEAS Intenational Conference on Infornation Security and Privacy 1 Pages: 91-97
  • Peer Reviewed
• [Journal Article] Quantum Quasi-Cyclic LDPC Codes (2007)
  • Author(s): Manabu HAGIWARA, Hideki IMAI
  • Journal Title: Proceeding of 2007 IEEE International Symposium on Information Theory (to appear)
• [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
  • 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
  • NAID: 10016632488
  • 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, et al.
  • Journal Title: Proceeding of The 2006 International Symposium on Information Theory and its Applications 1(CD-ROM)
• [Journal Article] On the Correcting Property of a Two-dimensional Error-Correcting Code Based on the Lee Metric on Z _(2^m) (2006)
  • Author(s): Banri Bannai, Manabu HAGIWARA, et al.
  • Journal Title: Proceeding of The 2006 International Symposium on Information Theory and its Applications 1(CD-ROM)
• [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-FUNDMENTAL ELECTRONIC SCIENCE Apr-90 Pages: 63-68
  • NAID: 10016632488
• [Presentation] A Study on a Key Establishment Scheme with QC LDPC Codes and UH-Protocols (2008)
  • Author(s): Yuto Matsunaga, M.Hagiwara, K.Kobara, H.Imai
  • Organizer: ISITA 2008
  • Place of Presentation: ニュージーランド、オークランド
  • Year and Date: 2008-12-08
• [Presentation] LDPC符号の各ビット位置のエラー率を求めるシミュレーションの高速化の検討 (2008)
  • Author(s): 松永雄斗、萩原学
  • Organizer: LDPC符号ワークショップ
  • Place of Presentation: 沖縄県
  • Year and Date: 2008-09-11
• [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] 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: COS08
  • Place of Presentation: 沖縄県
  • Year and Date: 2008-09-09
• [Presentation] 誤り訂正とプライバシ増幅の関係についての検討 (2008)
  • Author(s): 松永 雄斗、萩原 学、美添 一樹、古原 和邦、今井 秀樹
  • Organizer: 暗号と情報セキュリティシンポジウム(SCIS2008)
  • Place of Presentation: 宮崎県
  • Year and Date: 2008-01-22
• [Presentation] A Quantum Secure Direct Communication Protocol for Sending A Quantum State and Its Security Analysis (2007)
  • Author(s): Yumiko Murakami, Masaki Nakanishi, Manabu Hagiwara, Shigeru Yamashita, Yasuhiko Nakashima
  • Organizer: The 6th WSEAS International Conference on information Security and Privacy
  • Place of Presentation: スペイン
  • Year and Date: 2007-12-17
• [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] 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(SITA2007)
  • Place of Presentation: 三重県
  • Year and Date: 2007-11-27
• [Presentation] LDPC符号を用いた可変指向性アンテナを用いた秘密鍵共有システムの雑音除去 (2007)
  • Author(s): 松永 雄斗、萩原 学、古原 和邦、今井 秀樹
  • Organizer: 情報理論とその応用シンポジウム(SITA2007)
  • Place of Presentation: 三重県
  • Year and Date: 2007-11-27
• [Presentation] 非正則疑似巡薗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 (2007)
  • Author(s): 萩原 学
  • Organizer: 組合せ論サマースクール2007
  • Place of Presentation: 沖縄県
  • Year and Date: 2007-09-04
• [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 Error-Correcting Codes (2007)
  • Author(s): Manabu Hagiwara
  • Organizer: Summer School on Mathemtical Aspects of Quantum Computing
  • Place of Presentation: 近畿大学
  • 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] Quantum Quasi-Cyclic LDPC codes (2007)
  • Author(s): Manabu Hagiwara, Hideki Imai
  • Organizer: 2007 IEEE International Symposium on Information Theory
  • Place of Presentation: ニース
  • Year and Date: 2007-06-26
• [Presentation] A Simple Construction of Quantum Quasi-Cyclic LDPC codes (2007)
  • Author(s): Manabu Hagiwara, Hideki Imai
  • Organizer: 2007 Hawaii and SITA Joint Conference on Infor mation Theory
  • Place of Presentation: ハワイ大学
  • Year and Date: 2007-05-29
• [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
• [Remarks]
  • URL: http://staff.aist.go.jp/hagiwara.hagiwara/qecc/qecc.html
• [Remarks]
  • URL: http://staff.aist.go.jp/hagiwara.hagiwara/qecc/qecc.html