access icon free Sampled-data design for robust control of open two-level quantum systems with operator errors

This study proposes a sampled-data design method for robust control of open two-level quantum systems with operator errors. The required control performance is characterised using the concept of a sliding mode domain related to fidelity, coherence or purity. The authors have designed a control law offline and then utilise it online for a two-level system subject to decoherence with operator errors in the system model. They analyse three cases of approximate amplitude damping decoherence, approximate phase damping decoherence and approximate depolarising decoherence. They design specific sampling periods for these cases that can guarantee the required control performance.

Inspec keywords: robust control; sampled data systems; control system synthesis

Other keywords: operator errors; open two-level quantum systems; sliding mode domain; sampled-data design method; approximate amplitude damping decoherence; approximate phase damping decoherence; robust control; approximate depolarising decoherence

Subjects: Discrete control systems; Stability in control theory; Control system analysis and synthesis methods

References

    1. 1)
      • 2. Wiseman, H.M., Milburn, G.J.: ‘Quantum measurement and control’ (Cambridge University Press, Cambridge, England, 2010).
    2. 2)
      • 27. Ticozzi, F., Viola, L.: ‘Quantum Markovian subsystems: invariance’, attractivity, and control', IEEE Trans. Autom. Control, 2008, 53, pp. 20482063.
    3. 3)
      • 35. Beige, A., Braun, D., Tregenna, B., et al: ‘Quantum computing using dissipation to remain in a decoherence-free subspace’, Phys. Rev. Lett., 2000, 85, pp. 17621765.
    4. 4)
      • 25. Viola, L., Knill, E., Lloyd, S.: ‘Dynamical decoupling of open quantum systems’, Phys. Rev. Lett., 1999, 82, pp. 24172421.
    5. 5)
      • 5. D'Alessandro, D.: ‘Introduction to quantum control and dynamics’ (Chapman & Hall/CRC, 2007).
    6. 6)
      • 26. Qi, B.: ‘A two-step strategy for stabilizing control of quantum systems with uncertainties’, Automatica, 2013, 49, pp. 834839.
    7. 7)
      • 37. Lidar, D.A., Schneider, S.: ‘Stabilizing qubit coherence via tracking-control’, Quantum Inf. Comput., 2005, 5, pp. 350363.
    8. 8)
      • 6. Boscain, U., Mason, P.: ‘Time minimal trajectories for a spin 1/2 particle in a magnetic field’, J. Math. Phys., 2006, 47, p. 062101.
    9. 9)
      • 12. Sayrin, C., Dotsenko, I., Zhou, X., et al: ‘Real-time quantum feedback prepares and stabilizes photon number states’, Nature, 2011, 477, pp. 7377.
    10. 10)
      • 9. van Handel, R., Stockton, J.K., Mabuchi, H.: ‘Feedback control of quantum state reduction’, IEEE Trans. Autom. Control, 2005, 50, (6), pp. 768780.
    11. 11)
      • 8. Doherty, A.C., Habib, S., Jacobs, K., et al: ‘Quantum feedback control and classical control theory’, Phys. Rev. A, 2000, 62, p. 012105.
    12. 12)
      • 29. Dong, D., Petersen, I.R., Rabitz, H.: ‘Sampled-data design for robust decoherence control of a single qubit’. Proc. of 51st IEEE Conf. on Decision and Control, Maui, USA, 10–13 December 2012, pp. 16681673.
    13. 13)
      • 33. Maalouf, A.I., Petersen, I.R.: ‘Sampled-data LQG control for a class of linear quantum systems’, Syst. Control Lett., 2012, 61, pp. 369374.
    14. 14)
      • 3. Altafini, C., Ticozzi, F.: ‘Modeling and control of quantum systems: an introduction’, IEEE Trans. Autom. Control, 2012, 57, pp. 18981917.
    15. 15)
      • 22. Breuer, H.-P., Petruccione, F.: ‘The theory of open quantum systems’ (Oxford University Press, Oxford, UK, 2002, 1st edn.).
    16. 16)
      • 24. Knill, E., Laflamme, R., Viola, L.: ‘Theory of quantum error correction for general noise’, Phys. Rev. Lett., 2000, 84, pp. 25252528.
    17. 17)
      • 31. Dong, D., Petersen, I.R.: ‘Notes on sliding mode control of two-level quantum systems’, Automatica, 2012, 48, pp. 30893097.
    18. 18)
      • 14. Qi, B., Guo, L.: ‘Is measurement-based feedback still better for quantum control systems?’, Syst. Control Lett., 2010, 59, pp. 333339.
    19. 19)
      • 18. Dong, D., Petersen, I.R.: ‘Sliding mode control of two-level quantum systems’, Automatica, 2012, 48, pp. 725735.
    20. 20)
      • 11. Qi, B., Pan, H., Guo, L.: ‘Further results on stabilizing control of quantum system’, IEEE Trans. Autom. Control, 2013, 58, (5), pp. 13491354.
    21. 21)
      • 13. Mirrahimi, M., van Handel, R.: ‘Stabilizing feedback controls for quantum systems’, SIAM Optim. Control, 2007, 46, (2), pp. 445467.
    22. 22)
      • 36. Lindblad, G.: ‘On the generators of quantum dynamical semigroups’, Commun. Math. Phys., 1976, 48, pp. 119130.
    23. 23)
      • 20. Chen, C., Dong, D., Long, R., et al: ‘Sampling-based learning control of inhomogeneous quantum ensembles’, Phys. Rev. A, 2014, 89, p. 023402.
    24. 24)
      • 16. James, M.R.: ‘Risk-sensitive optimal control of quantum systems’, Phys. Rev. A, 2004, 69, p. 032108.
    25. 25)
      • 19. Soare, A., Ball, H., Hayes, D., et al: ‘Experimental noise filtering by quantum control’, Nat. Phys., 2014, 10, pp. 825829.
    26. 26)
      • 28. Dong, D., Petersen, I.R., Rabitz, H.: ‘Sampled-data design for robust control of a single qubit’, IEEE Trans. Autom. Control, 2013, 58, pp. 26542659.
    27. 27)
      • 38. Zhang, J., Wu, R.B., Li, C.W., et al: ‘Protecting coherence and entanglement by quantum feedback controls’, IEEE Trans. Autom. Control, 2010, 55, (3), pp. 619633.
    28. 28)
      • 17. Dong, D., Petersen, I.R.: ‘Sliding mode control of quantum systems’, New J. Phys., 2009, 11, p. 105033.
    29. 29)
      • 34. Itano, W.M., Heinzen, D.J., Bollinger, J.J., et al: ‘Quantum Zeno effect’, Phys. Rev. A, 1990, 41, pp. 22952300.
    30. 30)
      • 15. James, M.R., Nurdin, H.I., Petersen, I.R.: ‘H control of linear quantum stochastic systems’, IEEE Trans. Autom. Control, 2008, 53, pp. 17871803.
    31. 31)
      • 32. Dong, D., Petersen, I.R., Yi, X.X., et al: ‘Sampled-data design for decoherence control of a single qubit with operator errors’. Proc. of 2012 Australian Control Conf., Sydney, Australia, 15–16 November 2012, pp. 1318.
    32. 32)
      • 21. Dong, D., Chen, C., Qi, B., et al: ‘Robust manipulation of superconducting qubits in the presence of fluctuations’, Sci. Rep., 2015, 5, p. 7873.
    33. 33)
      • 30. Wang, Y., Chen, C., Dong, D.: ‘Further results on sampled-data design for robust control of a single qubit’, Int. J. Control, 2014, 87, pp. 20562064.
    34. 34)
      • 23. Lidar, D.A., Chuang, I.L., Whaley, K.B.: ‘Decoherence-free subspaces for quantum computation’, Phys. Rev. Lett., 1999, 81, pp. 25942597.
    35. 35)
      • 4. Nielsen, M.A., Chuang, I.L.: ‘Quantum Computation and Quantum Information’ (Cambridge University Press, Cambridge, England, 2000).
    36. 36)
      • 10. Shabani, A., Jacobs, K.: ‘Locally optimal control of quantum systems with strong feedback’, Phys. Rev. Lett., 2008, 101, p. 230403.
    37. 37)
      • 7. Fu, S., Chen, M.Z.Q.: ‘Optimal control of single spin- 1/2 quantum systems’, IET Control Theory Appl., 2014, 8, pp. 8693.
    38. 38)
      • 1. Dong, D., Petersen, I.R.: ‘Quantum control theory and applications: a survey’, IET Control Theory Appl., 2010, 4, pp. 26512671.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.0368
Loading

Related content

content/journals/10.1049/iet-cta.2016.0368
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading