Information and Communications Magazine (정보와 통신)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

Graph state 기법을 이용한 6-큐비트 양자 오류 정정 부호 설계

  • Published : 2015.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

본 고에서는 그래프 상태(graph state)를 이용하여 양 자 오류 정정 부호를 설계하는 기법에 대해서 알아본다. 그래프 상태는 꼭짓점과 각 꼭짓점을 연결하는 변으로 구성된다. 그래프 상태에서 각 꼭지점은 실제 코드워드의 각 큐비트에 해당하며 꼭지 점을 연결하는 변은 양자 오류 정정 부호의 부호화 방식을 결정한다. 본 고에서는 그래프 상태의 특성을 알아보고 그래프 상태 기반 양자 오류 정정 부호 설계 기법을 이용하여 단일 오류를 검출할 수 있는 6-큐비트 양자 오류 정정 부호 설계 방법에 대해 알아본다.

Keywords

References

  1. P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A, vol. 52, no. 4, pp. R2493-R2496, Oct. 1995. https://doi.org/10.1103/PhysRevA.52.R2493
  2. D. Gottesman, "Stabilizer codes and quantum error correction," Ph.D. dissertation, Caltech Ph.D. dissertation, Psadena, CA, May 1997.
  3. A. Calderbank and P. W. Shor, "Good quantum error-correcting codes exist," Phys. Rev. A, vol. 54, no. 2, pp. 1098-1105, Aug. 1996. https://doi.org/10.1103/PhysRevA.54.1098
  4. A. Steane, "Multiple-Particle Interference and Quantum Error Correction," Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 452, no. 1954, pp. 2551-2577, 1996.
  5. M. Grassl, T. Beth, and T. Pellizzari, "Codes for the quantum erasure channel," Phys.Rev. A, vol. 56, pp. 33-38, Jul. 1997. https://doi.org/10.1103/PhysRevA.56.33
  6. A. Y. Kitaev, "Quantum Error Correction with Imperfect Gates," Quantum Communication, Computing, and Measurement, no. Chapter 19, pp. 181-188, 1997.
  7. A. Calderbank, E. M. M. Rains, P. W. Shor, and N. Sloane, "Quantum error correction via codes over GF(4)," IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1369-1387, Jul. 1998. https://doi.org/10.1109/18.681315
  8. M. Grassl and T. Beth, "A note on non-additive quantum codes," arXiv preprint quant-ph, 1997.
  9. E. M. M. Rains, R. H. Hardin, P. W. Shor, and N. Sloane, "Nonadditive Quantum Code," Phys. Rev. Lett., vol. 79, no. 5, pp. 953-954, Aug. 1997. https://doi.org/10.1103/PhysRevLett.79.953
  10. M.Grassl and M.Rotteler, "Non-additive quantum codes from Goethals and Preparata codes," Information Theory Workshop, 2008. ITW '08. IEEE, pp. 396-400, May 2008.
  11. M.Grassl and M.Rotteler, "Quantum Goethals-Preparata codes," Information Theory, 2008. ISIT 2008. IEEE International Symposium on, pp. 300-304, Jul. 2008.
  12. S. Yu, Q. Chen, C.-Y. Lai, and C. H. Oh, "Nonadditive Quantum Error-Correcting Code," Phys. Rev. Lett., vol. 101, no. 9, p. 090501, Aug. 2008. https://doi.org/10.1103/PhysRevLett.101.090501
  13. A. Cross, G. Smith, J. A. Smolin, and B. Zeng, "Codeword Stabilized Quantum Codes," IEEE Transactions on Information Theory, vol. 55, no. 1, pp. 433-438, Jan. 2009. https://doi.org/10.1109/TIT.2008.2008136
  14. J. Shin, J. Heo, and T. A. Brun, "Entanglement-assisted codeword stabilized quantum codes," Phys. Rev. A, vol. 84, p. 062321, Dec. 2011. https://doi.org/10.1103/PhysRevA.84.062321
  15. M. Van den Nest, J. Dehaene, and B. De Moor, "Graphical description of the action of local Clifford transformations on graph states," Phys. Rev. A, vol. 69, no. 2, p. 022316, Feb. 2004. https://doi.org/10.1103/PhysRevA.69.022316
  16. M. Hein, J. Eisert, and H. J. Briegel, "Multiparty entanglement in graph states," Phys. Rev. A, vol. 69, p. 062311, Jun. 2004. https://doi.org/10.1103/PhysRevA.69.062311
  17. S. Yu, Q. Chen, and C. H. Oh. (2007, Sep.) Graphical Quantum Error-Correcting Codes. Online available at http://arxiv.org/abs/0709.1780v1
  18. D. Schlingemann and R. F. Werner, "Quantum error-correcting codes associated with graphs," Phys. Rev. A, vol. 65, p. 012308, Dec. 2001. https://doi.org/10.1103/PhysRevA.65.012308
  19. M. Grassl, "Bounds on the minimum distance of linear codes and quantum codes," Online available at http://www.codetables.de, 2007.