Skip to main content
Log in

Exact master equation and non-markovian decoherence for quantum dot quantum computing

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this article, we report the recent progress on decoherence dynamics of electrons in quantum dot quantum computing systems using the exact master equation we derived recently based on the Feynman–Vernon influence functional approach. The exact master equation is valid for general nanostructure systems coupled to multi-reservoirs with arbitrary spectral densities, temperatures and biases. We take the double quantum dot charge qubit system as a specific example, and discuss in details the decoherence dynamics of the charge qubit under coherence controls. The decoherence dynamics risen from the entanglement between the system and the environment is mainly non-Markovian. We further discuss the decoherence of the double-dot charge qubit induced by quantum point contact (QPC) measurement where the master equation is re-derived using the Keldysh non-equilibrium Green function technique due to the non-linear coupling between the charge qubit and the QPC. The non-Markovian decoherence dynamics in the measurement processes is extensively discussed as well.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Tu M.W.Y., Zhang W.M.: Non-Markovian decoherence theory for a double-dot charge qubit. Phys. Rev. B 78, 235311 (2008)

    Article  ADS  Google Scholar 

  2. Feynman R.P., Vernon F.L.: The theory of a general quantum system interacting with a linear dissipative system. Ann. Phys. 24, 118 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  3. Legget A.J., Chakravarty S., Dorsey A.T., Fisher M.P.A., Garg A., Zwerger W.: Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59, 1 (1987)

    Article  ADS  Google Scholar 

  4. Zurek W.H.: Decoherence and the transition from quantum to classical. Phys. Today 44(10), 36 (1991)

    Article  Google Scholar 

  5. Zurek W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  6. Caldeira A.O., Leggett A.J.: Path integral approach to quantum Brownian motion. Physica A 121, 587 (1983)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Hu B.L., Paz J.P., Zhang Y.H.: Quantum Brownian motion in a general environment: exact master equation with nonlocal dissipation and colored noise. Phys. Rev. D 45, 2843 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  8. Weiss U.: Quantum Dissipative Systems. World Scientific, Singapore (1999)

    MATH  Google Scholar 

  9. Breuer H.P., Petruccione F.: The theory of open quantum systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  10. Calzetta E., Hu B.L.: Nonequilibrium quantum field theory. Cambridge University Press, New York (2008)

    MATH  Google Scholar 

  11. Chou C.H., Yu T., Hu B.L.: Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment. Phys. Rev. E 77, 011112 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  12. An J.H., Zhang W.M.: Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels. Phys. Rev. A 76, 042127 (2007)

    Article  ADS  Google Scholar 

  13. An J.H., Feng M., Zhang W.M.: Non-Markovian decoherence dynamics of entangled coherent states. Quantum Inf. Comput. 9, 0317 (2009)

    CAS  Google Scholar 

  14. Zhang W.M., Feng D.H., Gilmore R.: Coherent states: theory and some applications. Rev. Mod. Phys. 62, 867 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  15. Gurvitz S.A.: Measurements with a noninvasive detector and dephasing mechanism. Phys. Rev. B 56, 15215 (1997)

    Article  CAS  ADS  Google Scholar 

  16. Goan H.S., Milburm G.J., Wiseman H.M., Sun H.B.: Continuous quantum measurement of two coupled quantum dots using a point contact: a quantum trajectory approach. Phys. Rev. B 63, 125326 (2001)

    Article  ADS  Google Scholar 

  17. Lee M.T., Zhang M.W.: Decoherence induced by electron accumulation in a quantum measurement of charge qubits. Phys. Rev. B 74, 085325 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  18. Lee M.T., Zhang W.M.: Non-equilibrium theory of charge qubit decoherence in the quantum point contact measurement, arXiv: 0708.2581 (2007)

  19. Lee M.T., Zhang W.M.: Non-Markovian suppression of charge qubit decoherence in the quantum point contact measurement. J. Chem. Phys. 129, 224106 (2008)

    Article  PubMed  ADS  Google Scholar 

  20. Keldysh L.V.: Diagram technique for nonequilibrium processes. Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP, 20, 1018 (1965)]

    Google Scholar 

  21. Chou K.C., Su Z.B., Hao B.L., Yu L.: Equilibrium and nonequilibrium formalisms made unified. Phys. Rep. 118, 1 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  22. Rammer J., Smith H.: Quantum field–theoretical methods in transport theory of metals. Rev. Mod. Phys. 58, 323 (1986)

    Article  CAS  ADS  Google Scholar 

  23. Haug H., Jauho A.P.: Quantum Kinetics in Transport and Optics of Semiconductors. Springer, Berlin (1996)

    Google Scholar 

  24. Schoeller H., Schön G.: Mesoscopic quantum transport: resonant tunneling in the presence of a strong Coulomb interaction. Phys. Rev. B 50, 18436 (1994)

    Article  CAS  ADS  Google Scholar 

  25. Schoeller H., König J.: Real-time renormalization group and charge fluctuations in quantum dots. Phys. Rev. Lett. 84, 3686 (2000)

    Article  CAS  PubMed  ADS  Google Scholar 

  26. Fujisawa T., Hayashi T., Sasaki S.: Time-dependent single-electron transport through quantum dots. Rep. Prog. Phys. 69, 759 (2006)

    Article  ADS  Google Scholar 

  27. Stoof T.H., Nazarov Y.V.: Time-dependent resonant tunneling via two discrete states. Phys. Rev. B 53, 1050 (1996)

    Article  CAS  ADS  Google Scholar 

  28. Gurvitz S.A., Prager Y.S.: Microscopic derivation of rate equations for quantum transport. Phys. Rev. B 53, 15932 (1996)

    Article  CAS  ADS  Google Scholar 

  29. Brandes T., Vorrath T.: Adiabatic transfer of electrons in coupled quantum dots. Phys. Rev. B 66, 075341 (2002)

    Article  ADS  Google Scholar 

  30. Yu T., Eberly J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)

    Article  PubMed  ADS  Google Scholar 

  31. Bellomo B., Lo Franco R., Compagno G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99, 160502 (2007)

    Article  CAS  PubMed  ADS  Google Scholar 

  32. Petta J.R., Johnson A.C., Taylor J.M., Laird E.A., Yacoby A., Lukin M.D., Marcus C.M., Hanson M.P., Gossard A.C.: Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180 (2005)

    Article  CAS  PubMed  ADS  Google Scholar 

  33. Zhang W.M., Wu Y.Z., Soo C., Feng M.: Charge-to-spin conversion of electron entangled states and spin-interaction-free solid-state quantum computation. Phys. Rev. B 76, 165311 (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wei-Min Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tu, M.WY., Lee, MT. & Zhang, WM. Exact master equation and non-markovian decoherence for quantum dot quantum computing. Quantum Inf Process 8, 631–646 (2009). https://doi.org/10.1007/s11128-009-0143-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-009-0143-8

Keywords

PACS

Navigation