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On the Construction of Quantum Error-Correcting Codes

Research Project

Project/Area Number 10650362
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 情報通信工学
Research InstitutionKOBE UNIVERSITY

Principal Investigator

TOKIWA Kin-ichiroh  Kobe University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70172145)

Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2000: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsQuantum Errors / QEC Codes / Quantum Computer / Quantum Communication / Quantum Coding Theory / Quantum Information Theory / Error Correction / Coding Theory
Research Abstract

Quantum error-correcting codes have been developed as one of the promising methods for protecting quantum information against quantum errors. One of the most important families of quantum error-correcting codes has been provided by Steane and Calderbank & Shor. In general, the resulting quantum error-correcting codes are commonly referred to as Calderbank-Shor-Steane (CSS) codes. A great deal of effort has been made to construct efficient quantum error-correcting codes from classical linear codes, and various code constructions have been proposed based on the CSS code construction. Especially, Vatan, Roychowdhury and Anantram have presented two types of revised versions of the CSS code construction, and have also provided an exhaustive procedure for determining bases of quantum error-correcting codes. Their results are very attractive because they can be applied to any set of quantum errors such as quantum random errors, quantum burst errors, and so on.
In this research, we have investigated in details the results and the searching procedure given by Vatan et al. As a result, we have pointed out that there is no essential difference between those revised versions. Moreover, by utilizing some fundamental properties of classical linear codes, we have proposed an efficient algorithm for searching for bases of CSS type quantum error-correcting codes. The proposed algorithm has much lower complexity than Vatan et al.'s procedure, and seems to be very useful in determining bases of quantum error-correcting codes constructed from classical linear codes which are not weakly self-dual. We have also shown some results of a computer search for new CSS type quantum burst-error-correcting codes obtained from classical cyclic codes of length 30 or less.

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (9 results)

All Other

All Publications (9 results)

  • [Publications] K.Tokiwa: "A Search Algorithm for Bases of Quantum Error-Correcting Codes"電子情報通信学会技術研究報告IT2000-4. 100・65. 19-24 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 佐田野佑介: "量子バースト誤り訂正符号の計算機探索"電子情報通信学会技術研究報告IT2000-27. 100・241. 7-12 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Tokiwa: "A Search Algorithm for Bases of Calderbank-Shor-Steane Type Quantum Error-Correcting Codes"IEICE Transactions on Fundamentals. E84-A・3. 860-865 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kin-ichiroh TOKIWA: "A Search Algorithm for Bases of Quantum Error-Correcting Codes"Technical Report of IEICE, IT2000-4. Vol.100, No.65. 19-24 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yuusuke SADANO: "Computer Search for Quantum Burst-Error-Correcting Codes"Technical Report of IEICE, IT2000-27. Vol.100, No.241. 7-12 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kin-ichiroh TOKIWA: "A Search Algorithm for Bases of Calderbank-Shor-Steane Type Quantum Error-Correcting Codes"IEICE Transactions on Fundamentals. Vol.E84-A,No.3. 860-865 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Tokiwa: "A Search Algorithm for Bases of Quantum Error-Correcting Codes"電子情報通信学会技術研究報告IT2000-4. 100・65. 19-24 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 佐田野佑介: "量子バースト誤り訂正符号の計算機探索"電子情報通信学会技術研究報告IT2000-27. 100・241. 7-12 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Tokiwa: "A Search Algorithm for Bases of Calderbank-Shor-Steane Type Quantum Error-Correcting Codes"IEICE Transactions on Fundamentals. E84-A・3. 860-865 (2001)

    • Related Report
      2000 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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