Skip to main content
SpringerLink
Log in

An interleaved sampling scheme for the characterization of single qubit dynamics

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we demonstrate that interleaved sampling techniques can be used to characterize the Hamiltonian of a qubit and its environmental decoherence rate. The technique offers a significant advantage in terms of the number of measurements that are required to characterize a qubit. When compared to the standard Nyquist–Shannon sampling rate, the saving in the total measurement time for the interleaved method is approximately proportional to the ratio of the sample rates.

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. Nakamura Y., Pashkin Y.A., Tsai J.S.: Coherent control of macroscopic quantum states in a single-cooper-pair box. Nature 398, 786–788 (1999)

    Article  ADS  Google Scholar 

  2. Pashkin Y.A., Yamamoto T., Astafiev O., Nakamura Y., Averin D.V., Tsai J.S.: Quantum oscillations in two coupled charge qubits. Nature 421, 823–826 (2003)

    Article  ADS  MATH  Google Scholar 

  3. Duty T., Gunnarsson D., Bladh K., Delsing P.: Coherent dynamics of a josephson charge qubit. Phys. Rev. B 69, 140503 (2004)

    Article  ADS  Google Scholar 

  4. Schirmer S.G., Kolli A., Daniel K.L.O.: An efficient measurement scheme for the charaterization of single qubit dynamics. Phys. Rev. A 69, 050306(R) (2004)

    Article  ADS  Google Scholar 

  5. Cole J.H., Schirmer S.G., Greentree A.D., Wellard C.J., Daniel K.L.O., Hollenberg L.C.L.: Identifying an experimental two-state hamiltonian to arbitrary accuracy. Phys. Rev. A 71, 062312 (2005)

    Article  ADS  Google Scholar 

  6. Cole J.H., Greentree A.D., Daniel K.L.O., Schirmer S.G., Wellard C.J., Hollenberg L.C.L.: Identifying a two-state hamiltonian in the presence of decoherence. Phys. Rev. A 73, 062333 (2006)

    Article  ADS  Google Scholar 

  7. Jerri A.J.: The shannon sampling theorem—its various extensions and applications: a tutorial review. Proc. IEEE 65, 1565–1596 (1977)

    Article  ADS  MATH  Google Scholar 

  8. Lathi B.P.: Modern Digital and Analog Communication Systems. 3rd edn. Oxford University Press, Oxford (1953)

    Google Scholar 

  9. Kohlenberg A.: Exact interpolation of band-limited functions. J. Appl. Phys. 24, 1432–1436 (1953)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Vaughan R.G., Scott N.L., Rod White D.: The theory of bandpass sampling. IEEE Trans. Signal Process. 39, 1973–1984 (1991)

    Article  ADS  Google Scholar 

  11. Ralph, J.F., Jacobs, K., Hill, C.D.: Frequency tracking and parameter estimation for robust quantum state-estimation. Eprint: quant-ph/0907.5034 (2009)

  12. Gambetta J., Wiseman H.M.: State and dynamical parameter estimation for open quantum systems. Phys. Rev. A 64, 042105 (2001)

    Article  ADS  Google Scholar 

  13. Wiseman H.M., Milburn G.J.: Quantum Measurement and Control. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  14. Huang D.: Approximate maximum likelihood method for frequency estimation. Stat. Sinica 10, 157–171 (2000)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Joshua Combes

    Present address: The Department of Physics and Astronomy, University of New Mexico, 1919 Lomas Blvd NE, Albuquerque, NM, 87131, USA

Authors and Affiliations

  1. Department of Electrical Engineering and Electronics, The University of Liverpool, Brownlow Hill, Liverpool, L69 3GJ, UK

    Jason F. Ralph

  2. Centre for Quantum Dynamics, Griffith University, Brisbane, QLD, 4111, Australia

    Joshua Combes & Howard M. Wiseman

Authors
  1. Jason F. Ralph
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joshua Combes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Howard M. Wiseman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jason F. Ralph.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ralph, J.F., Combes, J. & Wiseman, H.M. An interleaved sampling scheme for the characterization of single qubit dynamics. Quantum Inf Process 11, 1523–1531 (2012). https://doi.org/10.1007/s11128-011-0313-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-011-0313-3

Keywords

Search

Navigation