Advertisement

Quantum computing through electron propagation in edge states of quantum spin Hall systems

  • Wei Chen
  • Zheng-Yuan Xue
  • Z.D. Wang
  • Rui ShenEmail author
  • Ding Yu Xing
Regular Article

Abstract

We propose to implement quantum computing by the on-demand control of the wave packets propagation in helical edge channels of the quantum spin Hall systems (QSHs). Two non-commutative single-qubit gates are realized by the gate voltages applied on the edge channels. The two-qubit controlled phase gate is implemented by the capacitive Coulomb interaction between two adjacent edge channels from two parallel QSHs. A universal set of quantum gates thus can be realized in an all-electrical way. It is also shown that the fidelity and the purity of the controlled phase gate can reach a high value, with both the time delay and the finite width of the wave packets taken into account.

Keywords

Solid State and Materials 

References

  1. 1.
    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010) ADSCrossRefGoogle Scholar
  2. 2.
    X.L. Qi, S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011) ADSCrossRefGoogle Scholar
  3. 3.
    J. Maciejko, E.A. Kim, X.L. Qi, Phys. Rev. B 82, 195409 (2010) ADSCrossRefGoogle Scholar
  4. 4.
    V. Krueckl, K. Richter, Phys. Rev. Lett. 107, 086803 (2011) ADSCrossRefGoogle Scholar
  5. 5.
    W. Chen, R. Shen, L. Sheng, B.G. Wang, D.Y. Xing, Phys. Rev. Lett. 109, 036802 (2012) ADSCrossRefGoogle Scholar
  6. 6.
    W. Chen, Z.D. Wang, R. Shen, D.Y. Xing, arXiv:1304.5933 (2013) Google Scholar
  7. 7.
    L. Fu, C.L. Kane, Phys. Rev. Lett. 100, 096407 (2008) ADSCrossRefGoogle Scholar
  8. 8.
    L. Fu, C.L. Kane, Phys. Rev. B 79, 161408(R) (2009) ADSCrossRefGoogle Scholar
  9. 9.
    A.Y. Kitaev, Ann. Phys. 303, 2 (2003) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    C. Nayak, S.H. Simon, A. Stern, M. Freedman, S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998) ADSCrossRefGoogle Scholar
  12. 12.
    M. König, M.S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.L. Qi, S.C. Zhang, Science 318, 766 (2007) ADSCrossRefGoogle Scholar
  13. 13.
    I. Knez, R.R. Du, G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011) ADSCrossRefGoogle Scholar
  14. 14.
    I. Knez, R.R. Du, G. Sullivan, Phys. Rev. Lett. 109, 186603 (2012) ADSCrossRefGoogle Scholar
  15. 15.
    L.J. Du, I. Knez, G. Sullivan, R.R. Du, arXiv:1306.1925 (2013) Google Scholar
  16. 16.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000) Google Scholar
  17. 17.
    G. Fève, A. Mahe, J.M. Berroir, T. Kontos, B. Plaçais, D.C. Glattli, A. Cavanna, B. Etienne, Y. Jin, Science 316, 1169 (2007) ADSCrossRefGoogle Scholar
  18. 18.
    E. Bocquillon, V. Freulon, J.M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève, Science 339, 1054 (2013) ADSCrossRefGoogle Scholar
  19. 19.
    J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau, D.C. Glattli, Nature 502, 659 (2013) ADSCrossRefGoogle Scholar
  20. 20.
    F. Hassler, A.R. Akhmerov, C.-Y. Hou, C.W.J. Beenakker, New J. Phys. 12, 125002 (2010) ADSCrossRefGoogle Scholar
  21. 21.
    J.D. Sau, S. Tewari, S. Das Sarma, Phys. Rev. A 82, 052322 (2010) ADSCrossRefGoogle Scholar
  22. 22.
    L. Jiang, C.L. Kane, J. Preskill, Phys. Rev. Lett. 106, 130504 (2011) ADSCrossRefGoogle Scholar
  23. 23.
    P. Bonderson, R.M. Lutchyn, Phys. Rev. Lett. 106, 130505 (2011) ADSCrossRefGoogle Scholar
  24. 24.
    M. Leijnse, K. Flensberg, Phys. Rev. Lett. 107, 210502 (2011) ADSCrossRefGoogle Scholar
  25. 25.
    S. Bravyi, A. Kitaev, Phys. Rev. A 71, 022316 (2005) ADSCrossRefMathSciNetGoogle Scholar
  26. 26.
    P.P. Hofer, M. Büttiker, Phys. Rev. B 88, 241308(R) (2013) ADSCrossRefGoogle Scholar
  27. 27.
    A. Inhofer, D. Bercioux, Phys. Rev. B 88, 235412 (2013) ADSCrossRefGoogle Scholar
  28. 28.
    D.A. Ivanov, H.W. Lee, L.S. Levitov, Phys. Rev. B 56, 6839 (1997) ADSCrossRefGoogle Scholar
  29. 29.
    J. Dubois, T. Jullien, C. Grenier, P. Degiovanni, P. Roulleau, D.C. Glattli, Phys. Rev. B 88, 085301 (2013) ADSCrossRefGoogle Scholar
  30. 30.
    D. Ferraro, A. Feller, A. Ghibaudo, E. Thibierge, E. Bocquillon, G. Fève, Ch. Grenier, P. Degiovanni, Phys. Rev. B 88, 205303 (2013) ADSCrossRefGoogle Scholar
  31. 31.
    F. Dolcini, Phys. Rev. B 83, 165304 (2011) ADSCrossRefGoogle Scholar
  32. 32.
    F. Romeo, R. Citro, D. Ferraro, M. Sassetti, Phys. Rev. B 86, 165418 (2012) ADSCrossRefGoogle Scholar
  33. 33.
    J.C.Y. Teo, C.L. Kane, Phys. Rev. B 79, 235321 (2009) ADSCrossRefGoogle Scholar
  34. 34.
    J. Dressel, Y. Choi, A.N. Jordan, Phys. Rev. B 85, 045320 (2012) CrossRefGoogle Scholar
  35. 35.
    A.A. Vyshnevyy, A.V. Lebedev, G.B. Lesovik, G. Blatter, Phys. Rev. B 87, 165302 (2013) ADSCrossRefGoogle Scholar
  36. 36.
    A.V. Lebedev, G. Blatter, Phys. Rev. Lett. 107, 076803 (2011) ADSCrossRefGoogle Scholar
  37. 37.
    J.F. Poyatos, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 78, 390 (1997) ADSCrossRefGoogle Scholar
  38. 38.
    P. Virtanen, P. Recher, Phys. Rev. B 83, 115332 (2011) ADSCrossRefGoogle Scholar
  39. 39.
    J. Maciejko, C. Liu, Y. Oreg, X.L. Qi, C. Wu, S.C. Zhang, Phys. Rev. Lett. 102, 256803 (2009) ADSCrossRefGoogle Scholar
  40. 40.
    S. Mi, D.I. Pikulin, M. Wimmer, C.W.J. Beenakker, Phys. Rev. B 87, 241405(R) (2013) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Wei Chen
    • 1
    • 2
  • Zheng-Yuan Xue
    • 2
    • 3
  • Z.D. Wang
    • 2
  • Rui Shen
    • 1
    Email author
  • Ding Yu Xing
    • 1
  1. 1.National Laboratory of Solid State Microstructures and Department of Physics, Nanjing UniversityNanjingP.R. China
  2. 2.Department of Physics and Center of Theoretical and Computational PhysicsThe University of Hong KongHong KongP.R. China
  3. 3.Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal UniversityGuangzhouP.R. China

Personalised recommendations