The Journal of the Korea institute of electronic communication sciences (한국전자통신학회논문지)

Korea Institute of Electronic Communication Science (한국전자통신학회)
권호 표지
DOI QR코드

DOI QR Code

Augmented QSBC(Quantum Short-Block Code)-QURC(Quantum Unity-Rate Code)(II) with Pauli X,Y,Z error detection

파울리 X,Y,Z 오류검출 기능을 갖는 증강된 QSBC(Quantum Short-Block Code)-QURC(Quantum Unity-Rate Code)(II)

  • 박동영 (강릉원주대학교 정보통신공학과) ;
  • 서상민 (강릉원주대학교 정보통신공학과) ;
  • 김백기 (강릉원주대학교 정보통신공학과)
  • Received : 2023.04.10
  • Accepted : 2023.06.17
  • Published : 2023.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper proposes a method to find out the type and location information of Pauli X, Y, Z errors generated in quantum channels using only the quantum information processing part of the multiple-rate quantum turbo short-block code without external help from the classical information processing part. In order to obtain the location information of the Pauli X,Y error, n-auxiliary qubits and n-CNOT gates were inserted into the C[n,k,2] QSBC-QURC encoder. As a result, the maximum coding rate is limited to about 1/2 as the trade-off characteristics. The location information of the Pauli Z error for C[n,k,2] QSBC-QURC was obtained through the Clifford-based stabilizer measurement. The proposed method inherits all other characteristics of C[n,k,2] QSBC-QURC except for the coding rate.

본 논문은 멀티레이트 양자 터보 숏-블럭 코드의 양자정보처리 파트만을 이용해 고전정보처리 파트의 외부 도움 없이 양자 채널에서 발생한 파울리 X,Y,Z 오류의 유형과 위치 정보를 알아내는 방법을 제안한다. 파울리 X,Y 오류의 위치 정보를 얻기 위해 C[n,k,2] QSBC-QURC 인코더에 각각 n개의 보조 큐빗과 CNOT 게이트를 삽입했는데 그 결과 최대 코딩률이 약 1/2로 제한되는 절충 특성을 갖게 되었다. C[n,k,2] QSBC-QURC에 대한 파울리 Z 오류의 위치 정보는 클리포드 기반 스태빌라이저 측정으로 구했다. 제안한 방법은 코딩률 외의 C[n,k,2] QSBC-QURC가 가진 나머지 모든 특성을 상속한다.

Keywords

Acknowledgement

This study was supported by Gangneung-Wonju National University.

References

  1. V. Silva, Practical Quantum Computing for Developers: Programming Quantum Rigs in the Cloud using Python, Quantum Assembly Language and IBM Q Experience. Cary NC USA : APress, 2018.
  2. D. Gottesman, "Stabilizer Codes and Quantum Error Correction," Ph.D. Dissertation. (Advisor: John Preskill), California Institute of Technology, 1997.
  3. P. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A, Gen. Phys., vol. 52, no. 4, 1995. pp. 2493-2496. https://doi.org/10.1103/PhysRevA.52.R2493
  4. C. Wu, Y. Tsai, and H. Tsai, "Quantum circuits for stabilizer codes," In Proc. IEEE Int. Symp. on Circuits and Systems (ISCAS), Kobe, Japan, May 2005, pp. 2333-2336.
  5. D. Park and B. Kim, "New QECCs for Multiple Flip Error Correction," J. of the Korea Institute of Electronic Communication Science, vol. 14, no. 5, 2019, pp. 907-916.
  6. R. Anitha and B. Vijayalakshmi, "Simulation of quantum encoder & decoder with flip bit error correction using reversible quantum gates," Int. Conf. on Recent Trends in Electrical, Control and Communication (RTECC), Selangor, Malaysia, Mar. 2018, pp. 99-102.
  7. D. Park, S. Suh, and B. Kim "Augmented Quantum Short-Block Code with Single Bit-Flip Error Correction," J. of the Korea Institute of Electronic Communication Science, vol. 17, no. 1, 2022, pp. 31-40.
  8. M. Wilde, M. Hsieh, and Z. Babar, "Entanglement-Assisted Quantum Turbo Codes," IEEE J. of Trans. on Information Theory, vol. 60, no.2, 2014, pp.1203-222. https://doi.org/10.1109/TIT.2013.2292052
  9. Z. Babar, P. Botsinis, D.Alanis, S. X. Ng, and L. Hanjo, "The Road From Classical to Quantum Codes : A Hashing Bound Approaching Design Procedure," IEEE Access, vol. 3, 2015, pp.146-176. https://doi.org/10.1109/ACCESS.2015.2405533
  10. D. Chandra, Z. Babar, S. X. Ng, and L. Hanjo, "Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes," IEEE Access, vol. 7, 2019, pp. 52712-52730. https://doi.org/10.1109/ACCESS.2019.2911515
  11. Z. Babar, D. Chandra, H. V. Nguyen, P. Botsinis, D. Alanis, S. X. Ng, L. Hanjo, "Duality of Quantum and Classical Error Correction Codes : Design Principles and Examples," IEEE Communications Surveys & Tutorials, vol. 21, no. 1, 2019, pp. 970-1010. https://doi.org/10.1109/COMST.2018.2861361
  12. D. Park, "A New Function Embedding Method for the Multiple-Controlled Unitary Gate based on Literal Switch," J. of the Korea Institute of Electronic Communication Science, vol. 12, no. 1, 2017, pp. 101-107.
  13. D. Park, "Function Embedding and Projective Measurement of Quantum Gate by Probability Amplitude Switch," J. of the Korea Institute of Electronic Communication Science, vol. 12, no. 6, 2017, pp. 1027-1034.