Laser Physics

, Volume 20, Issue 5, pp 1203–1209 | Cite as

Quantum system identification by Bayesian analysis of noisy data: Beyond Hamiltonian tomography

  • S. G. Schirmer
  • D. K. L. Oi
Quantum Information Science


We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy data. Here we show how to generalize this approach to systems with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the process for a range of three-level quantum systems. The results suggest that the Bayesian estimation of the frequencies and dephasing rates is generally highly accurate and the main source of errors are errors in the reconstructed Hamiltonian basis.


Laser Physics Adaptive Sampling Open Quantum System Dephasing Rate Intrinsic Decoherence 
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  1. 1.
    I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44, 2455 (1997).ADSGoogle Scholar
  2. 2.
    J. F. Poyatos, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 78, 390 (1997).CrossRefADSGoogle Scholar
  3. 3.
    S. G. Schirmer, A. Kolli, and D. K. L. Oi, Phys. Rev. A 69, 050306(R) (2004).CrossRefADSGoogle Scholar
  4. 4.
    S. G. Schirmer, A. Kolli, D. K. L. Oi, and J. H. Cole, in Proc. of the 7th Int. Conf. QCMC, Glasgow 25–29 July 2004 (AIP, 2004).Google Scholar
  5. 5.
    J. H. Cole, S. G. Schirmer, A. D. Greentree, C. J. Wellard, D. K. L. Oi, and L. C. L. Hollenberg, Phys. Rev. A 71, 062312 (2005).CrossRefADSGoogle Scholar
  6. 6.
    J. H. Cole, A. D. Greentree, D. K. L. Oi, S. G. Schirmer, C. J. Wellard, and L. C. L. Hollenberg, Phys. Rev. A 73, 062333 (2006).CrossRefADSGoogle Scholar
  7. 7.
    S. J. Devitt, S. G. Schirmer, D. K. L. Oi, J. H. Cole, and L. C. L. Hollenberg, New J. Phys. 9, 384 (2007).CrossRefADSGoogle Scholar
  8. 8.
    S. G. Schirmer, D. K. L. Oi, and S. J. Devitt, J. Phys.: Conf. Ser. 107, 012011 (2008)CrossRefADSGoogle Scholar
  9. 9.
    S. G. Schirmer and D. K. L. Oi, Phys. Rev. A 80, 022333 (2009)CrossRefADSGoogle Scholar
  10. 10.
    G. Larry Bretthorst, Bayesian Spectrum Analysis and Parameter Estimation (Springer, Berlin, 1998).Google Scholar
  11. 11.
    C. G. Broyden, J. Inst. Math. App. 6, 76 (1970).zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    R. Fletcher, Comp. J. 13, 317 (1970).zbMATHCrossRefGoogle Scholar
  13. 13.
    D. Goldfarb, Math. Computat. 24, 23 (1970).zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    D. F. Shanno, Math. Computat. 24, 647 (1970).CrossRefMathSciNetGoogle Scholar
  15. 15.
    Z. Leghtas, M. Mirrahimi, and P. Rouchon, arXiv:0903.1011.Google Scholar
  16. 16.
    D. Burgarth, K. Maruyama, and F. Nori, Phys. Rev. A 79, 020305(R) (2009).ADSGoogle Scholar
  17. 17.
    D. Burgarth and K. Maruyama, New J. Phys. 11, 103019 (2009).CrossRefADSGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Department of Applied Maths and Theoretical PhysicsUniversity of CambridgeCambridgeUK
  2. 2.SUPA, Department of PhysicsUniversity of StrathclydeGlasgowUK

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