Skip to main content
SpringerLink
Log in

Quantum error correction in silicon charge qubits

  • Published:
Russian Microelectronics Aims and scope Submit manuscript

Abstract

The interaction of the quantum register with a noisy environment that leads to phase and bit errors is considered. Modeling of 5-qubit and 9-qubit error-correction algorithms for various environments is performed. It is shown that the use of the quantum correction leads to a quadratic decrease in the error probability. The efficiency of applying the 5-qubit algorithm of error correction for a silicon double-dot qubit is shown.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brandt, H.E., Qubit Devices and the Issue of Quantum Decoherence, Prog. Quantum Electron., 1999, vol. 22, p. 257.

    Article  Google Scholar 

  2. Divincenzo, D.P., The Physical Implementation of Quantum Computation, Fortschr. Phys., 2000, vol. 10, p. 771.

    Article  Google Scholar 

  3. Haar, D.T., Theory and Applications of the Density Matrix, Rep. Prog. Phys., 1961, vol. 24, p. 304.

    Article  Google Scholar 

  4. Blum, K., Density Matrix Theory and Applications, Springer, 2011, 3rd ed.

    Google Scholar 

  5. Nielsen, M.A. and Chuang, I.L., Quantum Computation and Quantum Information, Cambridge: Cambridge Univ., 2004.

    Google Scholar 

  6. Fedichkin, L., Polynomial Procedure of Avoiding Multiqubit Errors Arising Due to Qubit-Qubit Interaction, Quantum Comput. Comput., 2000, vol. 1, p. 84.

    Google Scholar 

  7. Ozhigov, Y. and Fedichkin, L., A Quantum Computer with Fixed Interaction Is Universal, JETP Lett., 2003, vol. 77, p. 328.

    Article  Google Scholar 

  8. Steane, A.M., Error Correcting Codes in Quantum Theory, Phys. Rev. Lett., 1996, vol. 77, p. 793.

    Article  MathSciNet  MATH  Google Scholar 

  9. Ekert, A. and Macchiavello, C., Quantum Error Correction for Communication, Phys. Rev. Lett., 1996, vol. 77, p. 2585.

    Article  Google Scholar 

  10. Gottesman, D., Stabilizer Codes and Quantum Error Correction, LANL E-print, 1997. ArXiv:quant-ph/9705052.

    Google Scholar 

  11. Hirvensalo, M., Quantum Error Correction, Citeseer, 1998.

    Google Scholar 

  12. Knill, E., Laflamme, R., and Viola, L., Theory of Quantum Error Correction for General Noise, Phys. Rev. Lett., 2000, vol. 84, p. 2525.

    Article  MathSciNet  MATH  Google Scholar 

  13. Gottesman, D., Fault-Tolerant Quantum Computation, LANL E-print, 2000. ArXiv:quant-ph/0004072.

    Google Scholar 

  14. Knill, E., Laflamme, R., Ashikhmin, A., Barnum, H., Viola, L., and Zurek, W.H., Introduction to Quantum Error Correction, LANL E-print, 2002. ArXiv:quantph/0207170.

    Google Scholar 

  15. Gottesman, D., Quantum Error Correction and Fault-Tolerance, LANL E-print, 2005. ArXiv:quant-ph/0507174.

    Google Scholar 

  16. Shor, P.W., Scheme for Reducing Decoherence in Quantum Computer Memory, Phys. Rev. A, 1995, vol. 52, p. 2493.

    Article  Google Scholar 

  17. DiVincenzo, D.P. and Shor, P.W., Phys. Rev. Lett., 1996, vol. 77, p. 3260.

    Article  Google Scholar 

  18. Holevo, A.S., Probabilistic and Statistical Aspects of Quantum Theory, Springer, 2011.

    Book  MATH  Google Scholar 

  19. Amosov, G.G. and Holevo, A.S., On the Multiplicativity Conjecture for Quantum Channels, LANL E-print, 2002. ArXiv:math-ph/0103015.

    Google Scholar 

  20. Preskill, J., Lecture Notes for Physics 229: Quantum Information and Computations, Calif. Inst. Technol., 1998.

    Google Scholar 

  21. Choi, M., Completely Positive Linear Maps on Complex Matrices, Linear Algebra Appl., 1975, vol. 10, p. 285.

    Article  MATH  Google Scholar 

  22. Kraus, K., States, Effects, and Operations. Lecture Notes in Physics, vol. 190, Springer, 1983.

  23. Fedichkin, L., Fedorov, A., and Privman, V., Robustness of Multiqubit Entanglement, Proc. SPIE—Int. Soc. Opt. Eng., 2003, vol. 5105, p. 243.

    Google Scholar 

  24. Li, C.-K., Nakahara, M., Poon, Y.-T., Sze, N.-S., and Tomita, H., Recovery in Quantum Error Correction for General Noise without Measurement, LANL E-print, 2011. ArXiv:quant-ph/1102.1618.

    Google Scholar 

  25. Tomita, H. and Nakahara, M., Unitary Quantum Error Correction without Error Detection, LANL E-print, 2011. ArXiv:quant-ph/1101.0413.

    Google Scholar 

  26. Fedichkin, L., Yanchenko, M., and Valiev, K.A., Coherent Charge Qubits Based on GaAs Quantum Dots with a Built-In Barrier, Nanotecnology, 2000, vol. 11, p. 387.

    Article  Google Scholar 

  27. Fedichkin, L. and Fedorov, A., Error Rate of a Charge Qubit Coupled to an Acoustic Phonon Reservoir, Phys. Rev. A, 2004, vol. 69, p. 032311.

    Article  Google Scholar 

  28. Fedichkin, L. and Fedorov, A., Study of Temperature Dependence of Electron-Phonon Relaxation and Dephasing in Semiconductor Double-Dot Nanostructures, IEEE Trans. Nanotechn., 2005, vol. 4, p. 65.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics and Technology, Russian Academy of Sciences, Nakhimovskii pr. 36/1, Moscow, 117218, Russia

    A. A. Melnikov & L. E. Fedichkin

  2. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow region, 141700, Russia

    A. A. Melnikov & L. E. Fedichkin

  3. NIX, Zvezdny boul. 19, Moscow, Russia

    L. E. Fedichkin

Authors
  1. A. A. Melnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. E. Fedichkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Melnikov.

Additional information

Original Russian Text © A.A. Melnikov, L.E. Fedichkin, 2013, published in Mikroelektronika, 2013, Vol. 42, No. 3, pp. 186–193.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Melnikov, A.A., Fedichkin, L.E. Quantum error correction in silicon charge qubits. Russ Microelectron 42, 148–154 (2013). https://doi.org/10.1134/S1063739713020078

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063739713020078

Keywords

Search

Navigation