Advertisement

The European Physical Journal Special Topics

, Volume 227, Issue 3–4, pp 203–216 | Cite as

Speeding up thermalisation via open quantum system variational optimisation

  • Nishchay Suri
  • Felix C. Binder
  • Bhaskaran Muralidharan
  • Sai Vinjanampathy
Regular Article
Part of the following topical collections:
  1. Quantum Systems In and Out of Equilibrium - Fundamentals, Dynamics and Applications

Abstract

Optimising open quantum system evolution is an important step on the way to achieving quantum computing and quantum thermodynamic tasks. In this article, we approach optimisation via variational principles and derive an open quantum system variational algorithm explicitly for Lindblad evolution in Liouville space. As an example of such control over open system evolution, we control the thermalisation of a qubit attached to a thermal Lindbladian bath with a damping rate γ. Since thermalisation is an asymptotic process and the variational algorithm we consider is for fixed time, we present a way to discuss the potential speedup of thermalisation that can be expected from such variational algorithms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Werschnik, E.K.U. Gross, J. Phys. B: At. Mol. Opt. Phys. 40, R175 (2007) ADSCrossRefGoogle Scholar
  2. 2.
    D. D’Alessandro, Introduction to quantum control and dynamics (Taylor & Francis, 2008) Google Scholar
  3. 3.
    C. Brif, R. Chakrabarti, H. Rabitz, New J. Phys. 12, 075008 (2010) ADSCrossRefGoogle Scholar
  4. 4.
    S.J. Glaser, U. Boscain, T. Calarco, C.P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny, F.K. Wilhelm, Eur. Phys. J. D 69, 279 (2015) ADSCrossRefGoogle Scholar
  5. 5.
    C.P. Koch, J. Phys.: Condens. Matter 28, 213001 (2016) ADSGoogle Scholar
  6. 6.
    A. Borzì, G. Ciaramella, M. Sprengel, Formulation and Numerical Solution of Quantum Control Problems (Philadelphia, 2017) Google Scholar
  7. 7.
    N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, S.J. Glaser, J. Magn. Reson. 172, 296 (2005) ADSCrossRefGoogle Scholar
  8. 8.
    M. Avriel, Nonlinear Programming: Analysis and Methods (Prentice-Hall, Englewood Cliffs, New Jersey, 2003) Google Scholar
  9. 9.
    T. Caneva, T. Calarco, S. Montangero, Phys. Rev. A 84, 022326 (2011) Google Scholar
  10. 10.
    D.J. Tannor, V. Kazakov, V. Orlov, in Time Dependent Quantum Molecular Dynamics, edited by J. Broeckhove, L. Lathouwers (Plenum Press, New York, 1992), pp. 347–360 Google Scholar
  11. 11.
    W. Zhu, J. Botina, H. Rabitz, J. Chem. Phys. 108, 1953 (1998) ADSCrossRefGoogle Scholar
  12. 12.
    W. Zhu, H. Rabitz, Phys. Rev. A 58, 4741 (1998) ADSCrossRefGoogle Scholar
  13. 13.
    Y. Ohtsuki, W.S. Zhu, H. Rabitz, Y. Ohtsuki, J. Chem. Phys. 110, 9825 (1999) ADSCrossRefGoogle Scholar
  14. 14.
    Y. Maday, G. Turinici, J. Chem. Phys. 118, 8191 (2003) ADSCrossRefGoogle Scholar
  15. 15.
    Y. Ohtsuki, G. Turinici, H. Rabitz, J. Chem. Phys. 120, 5509 (2004) ADSCrossRefGoogle Scholar
  16. 16.
    N. Rach, T. Calarco, S. Montangero, Phys. Rev. A 92, 062343 (2016) ADSCrossRefGoogle Scholar
  17. 17.
    R. Eitan, M. Mundt, D.J. Tannor, Phys. Rev. A 83, 053426 (2011) ADSCrossRefGoogle Scholar
  18. 18.
    D. Stefanatos, Phys. Rev. E 90, 012119 (2014) ADSCrossRefGoogle Scholar
  19. 19.
    M. Bathaee, A.R. Bahrampour, Phys. Rev. E 94, 022141 (2016) ADSCrossRefGoogle Scholar
  20. 20.
    R. Kosloff, Y. Rezek, Entropy 19, 136 (2017) ADSCrossRefGoogle Scholar
  21. 21.
    A. del Campo, J. Goold, M. Paternostro, Sci. Rep. 4, 6208 (2014) CrossRefGoogle Scholar
  22. 22.
    Y. Zheng, S. Campbell, G.D. Chiara, D. Poletti, G. De Chiara, D. Poletti, Phys. Rev. A 94, 042132 (2016) ADSCrossRefGoogle Scholar
  23. 23.
    S. Deng, A. Chenu, P. Diao, F. Li, S. Yu, I. Coulamy, A. del Campo, H. Wu, Sci. Adv. 4, eaar5909 (2018) ADSCrossRefGoogle Scholar
  24. 24.
    V. Mukherjee, A. Carlini, A. Mari, T. Caneva, S. Montangero, T. Calarco, R. Fazio, V. Giovannetti, Phys. Rev. A 88, 062326 (2013) ADSCrossRefGoogle Scholar
  25. 25.
    S. Deffner, S. Campbell, J. Phys. A: Math. Theor. 50, 453001 (2017) ADSCrossRefGoogle Scholar
  26. 26.
    L. Mandelstam, I. Tamm, J. Phys. 9, 249 (1945) Google Scholar
  27. 27.
    N. Margolus, L. Levitin, Physica D: Nonlinear Phenomena 120, 188 (1998) ADSCrossRefGoogle Scholar
  28. 28.
    S. Deffner, E. Lutz, J. Phys. A: Math. Theor. 46, 335302 (2013) CrossRefGoogle Scholar
  29. 29.
    I. Marvian, R.W. Spekkens, P. Zanardi, Phys. Rev. A 93, 052331 (2016) ADSCrossRefGoogle Scholar
  30. 30.
    F. Campaioli, F.A. Pollock, F.C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, K. Modi, Phys. Rev. Lett. 118, 150601 (2017) ADSCrossRefGoogle Scholar
  31. 31.
    D.P. Pires, M. Cianciaruso, L.C. Céleri, G. Adesso, D.O. Soares-Pinto, Phys. Rev. X2 6, 021031 (2016) Google Scholar
  32. 32.
    D. Mondal, C. Datta, S. Sazim, Phys. Lett. A 380, 689 (2016) ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    D. Mondal, A.K. Pati, Phys. Lett. A 380, 1395 (2016) ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    S. Deffner, New J. Phys. 19, 103018 (2017) ADSCrossRefGoogle Scholar
  35. 35.
    F.C. Binder, S. Vinjanampathy, K. Modi, J. Goold, New J. Phys. 17, 75015 (2015) CrossRefGoogle Scholar
  36. 36.
    F.C. Binder, Work, Heat, and Power of Quantum Processes, Ph.D. thesis, University of Oxford, 2016 Google Scholar
  37. 37.
    R. Uzdin, U. Günther, S. Rahav, N. Moiseyev, J. Phys. A: Math. Theor. 45, 415304 (2012) CrossRefGoogle Scholar
  38. 38.
    I.M. Gelfand, S.V. Fomin, Calculus of variations (Prentice-Hall, 1963) Google Scholar
  39. 39.
    E. Gerjuoy, A.R.P. Rau, L. Spruch, Rev. Mod. Phys. 55, 725 (1983) ADSCrossRefGoogle Scholar
  40. 40.
    D.M. Reich, M. Ndong, C.P. Koch, J. Chem. Phys. 136, 104103 (2012) ADSCrossRefGoogle Scholar
  41. 41.
    A. Bartana, R. Kosloff, D.J. Tannor, J. Chem. Phys. 106, 1435 (1997) ADSCrossRefGoogle Scholar
  42. 42.
    H.-P. Breuer, F. Petruccione, The theory of open quantum systems (Oxford University Press, 2002) Google Scholar
  43. 43.
    R. Alicki, J. Phys. A: Math. Gen. 12, L103 (1979) ADSCrossRefGoogle Scholar
  44. 44.
    E. Geva, R. Kosloff, J.L. Skinner, J. Chem. Phys. 102, 8541 (1995) ADSCrossRefGoogle Scholar
  45. 45.
    R. Kosloff, Entropy 15, 2100 (2013) ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    R. Alicki, R. Kosloff, https://doi.org/arXiv:1801.08314 (2018)
  47. 47.
    S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, Oxford, 1999) Google Scholar
  48. 48.
    T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, G.E. Santoro, Phys. Rev. Lett. 103, 240501 (2009) ADSCrossRefGoogle Scholar
  49. 49.
    A. Bartana, R. Kosloff, D.J. Tannor, J. Chem. Phys. 99, 196 (1993) ADSCrossRefGoogle Scholar
  50. 50.
    T. Schulte-Herbrüggen, A. Spörl, N. Khaneja, S.J. Glaser, J. Phys. B: At. Mol. Opt. Phys. 44, 154013 (2011) ADSCrossRefGoogle Scholar
  51. 51.
    F.F. Floether, P. de Fouquieres, S.G. Schirmer, New J. Phys. 14, 073023 (2012) ADSCrossRefGoogle Scholar
  52. 52.
    M.H. Goerz, D.M. Reich, C.P. Koch, New J. Phys. 16, 055012 (2014) ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    V. Cavina, A. Mari, A. Carlini, V. Giovannetti, https://doi.org/arXiv:1709.07400 (2017)
  54. 54.
    J. Goold, M. Huber, A. Riera, L. del Rio, P. Skrzypczyk, J. Phys. A: Math. Theor. 49, 143001 (2016) ADSCrossRefGoogle Scholar
  55. 55.
    S. Vinjanampathy, J. Anders, Contemp. Phys. 57, 545 (2016) ADSCrossRefGoogle Scholar
  56. 56.
    J. Millen, A. Xuereb, New J. Phys. 18, 011002 (2016) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Nishchay Suri
    • 1
    • 2
  • Felix C. Binder
    • 3
    • 4
  • Bhaskaran Muralidharan
    • 5
  • Sai Vinjanampathy
    • 1
    • 6
  1. 1.Department of PhysicsIndian Institute of Technology BombayMumbaiIndia
  2. 2.Department of PhysicsCarnegie-Mellon UniversityPittsburghUSA
  3. 3.School of Physical and Mathematical Sciences, Nanyang Technological UniversitySingaporeSingapore
  4. 4.Complexity Institute, Nanyang Technological UniversitySingaporeSingapore
  5. 5.Department of Electrical EngineeringIndian Institute of Technology BombayMumbaiIndia
  6. 6.Centre for Quantum Technologies, National University of SingaporeSingaporeSingapore

Personalised recommendations