Applied Physics B

, Volume 95, Issue 2, pp 195–203 | Cite as

The “arch” of simulating quantum spin systems with trapped ions

  • H. Schmitz
  • A. Friedenauer
  • C. Schneider
  • R. Matjeschk
  • M. Enderlein
  • T. Huber
  • J. Glueckert
  • D. Porras
  • T. Schaetz
Open Access
Article

Abstract

We cannot translate quantum behavior arising with superposition states or entanglement efficiently into the classical language of conventional computers  (Feynman et al. in Int. J. Theor. Phys. 21:467, 1982). A universal quantum computer could describe and help to understand complex quantum systems. But it is envisioned to become functional only within the next decade(s). A shortcut was proposed via simulating the quantum behavior of interest in another quantum system, where all relevant parameters and interactions can be controlled and observables of interest detected sufficiently well. For example simulating quantum spin systems within an architecture of trapped ions (Porras and Cirac in Phys. Rev. Lett. 92:207901, 2004). Here we specify how we simulate the spin and all necessary interactions and how we calibrate their amplitudes. For example via a two-ion phase-gate operation on two axial motional modes simultaneously at a fidelity exceeding 95%. We explain the complete mode of operation of a quantum simulator on the basis of our simple model case—the proof of principle experiment of simulating the transition of a quantum magnet from paramagnetic into entangled ferromagnetic order  (Friedenauer et al. in Nat. Phys. 4:757, 2008) and emphasize some of the similarities and differences with a quantum computer.

PACS

03.67.Pp 42.50.vk 75.10.Jm 77.80.Bh 

References

  1. 1.
    R.P. Feynman, Int. J. Theor. Phys. 21, 467 (1982) CrossRefMathSciNetGoogle Scholar
  2. 2.
    D. Porras, J.I. Cirac, Phys. Rev. Lett. 92, 207901 (2004) CrossRefADSGoogle Scholar
  3. 3.
    A. Friedenauer, H. Schmitz, J. Glueckert, D. Porras, T. Schaetz, Nat. Phys. 4, 757 (2008) CrossRefGoogle Scholar
  4. 4.
    R. Hooke, A Description of Helioscopes, and Some Other Instruments (London, 1675) Google Scholar
  5. 5.
    S. Lloyd, Science 273, 1073 (1996) CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    J.I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 4091 (1995) CrossRefADSGoogle Scholar
  7. 7.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, 1st edn. (Cambridge University Press, Cambridge, 2000) MATHGoogle Scholar
  8. 8.
    D. Leibfried, E. Knill, S. Seidelin, J. Britton, R.B. Blakestad, J. Chiaverini, D.B. Hume, W.M. Itano, J.D. Jost, C. Langer, R. Ozeri, R. Reichle, D.J. Wineland, Nature 438, 639 (2005) CrossRefADSGoogle Scholar
  9. 9.
    H. Haeffner, W. Hänsel, C.F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U.D. Rapol, M. Riebe, P.O. Schmidt, C. Becher, O. Gühne, W. Dür, R. Blatt, Nature 438, 643 (2005) CrossRefADSGoogle Scholar
  10. 10.
    J. Benhelm, Nat. Phys. 4, 463 (2008) CrossRefGoogle Scholar
  11. 11.
    D. Feder, Private communication (2007) Google Scholar
  12. 12.
    J.I. Cirac, Private communication (2006) Google Scholar
  13. 13.
    D. Porras, J.I. Cirac, Phys. Rev. Lett. 93, 263602 (2004) CrossRefADSGoogle Scholar
  14. 14.
    E. Jané, G. Vidal, W. Dür, P. Zoller, J.I. Cirac, quant-ph/0207011 (2002)
  15. 15.
    R.P. Feynman, F.L. Vernon, R.W. Hellwarth, J. Appl. Phys. 28, 49 (1957) CrossRefADSGoogle Scholar
  16. 16.
    L. Allen, J.H. Eberly, Optical Resonance and Two-Level Atoms (Dover, Mineola, 1987) Google Scholar
  17. 17.
    J. Bollinger, D.J. Heinzen, W.M. Itano, S.L. Gilbert, D.J. Wineland, IEEE Trans. Instrum. Meas. 40, 126 (1991) CrossRefGoogle Scholar
  18. 18.
    R. Blatt, P. Zoller, Eur. J. Phys. 9, 250 (1988) CrossRefGoogle Scholar
  19. 19.
    D.J. Wineland, C. Monroe, W.M. Itano, D. Leibfried, B. King, D.M. Meekhof, J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998) Google Scholar
  20. 20.
    D.J. Wineland, M. Barrett, J. Britton, J. Chiaverini, B. DeMarco, W.M. Itano, C. Langer, D. Leibfried, V. Meyer, T. Rosenband, T. Schätz, Philos. Trans. R. Soc. Lond. A 361, 1349 (2003) CrossRefADSGoogle Scholar
  21. 21.
    J. Chiaverini, Quantum Inf. Comput. 5, 419 (2005) MATHMathSciNetGoogle Scholar
  22. 22.
    D. Leibfried B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W.M. Itano, Nature 422, 412 (2003) CrossRefADSGoogle Scholar
  23. 23.
    T. Schaetz, A. Friedenauer, H. Schmitz, L. Petersen, S. Kahra, J. Mod. Opt. 54, 2317 (2007) CrossRefGoogle Scholar
  24. 24.
    S. Seidelin, J. Chiaverini, R. Reichle, J.J. Bollinger, D. Leibfried, J. Britton, J.H. Wesenberg, R.B. Blakestad, R.J. Epstein, D.B. Hume, W.M. Itano, J.D. Jost, C. Langer, R. Ozeri, N. Shiga, D.J. Wineland, Phys. Rev. Lett. 96, 253003 (2006) CrossRefADSGoogle Scholar
  25. 25.
    J.I. Cirac, P. Zoller, Nature 404, 579 (2000) CrossRefADSGoogle Scholar
  26. 26.
    J. Labaziewicz, Y. Ge, P. Antohi, D. Leibrandt, K.R. Brown, I.L. Chuang, Phys. Rev. Lett. 100, 013001 (2008) CrossRefADSGoogle Scholar
  27. 27.
    P.W. Anderson, Science 235, 1196 (1987) CrossRefADSGoogle Scholar
  28. 28.
    L. Lamata, J. Leon, T. Schaetz, E. Solano, Phys. Rev. Lett. 98, 253005 (2007) CrossRefADSGoogle Scholar
  29. 29.
    R. Schuetzhold, M. Uhlmann, L. Petersen, A. Friedenauer, H. Schmitz, T. Schaetz, Phys. Rev. Lett. 99, 201301 (2007) CrossRefADSGoogle Scholar
  30. 30.
    B.C. Travaglione, G.J. Milburn, Phys. Rev. A 65, 032310 (2002) CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • H. Schmitz
    • 1
  • A. Friedenauer
    • 1
  • C. Schneider
    • 1
  • R. Matjeschk
    • 1
  • M. Enderlein
    • 1
  • T. Huber
    • 1
  • J. Glueckert
    • 1
  • D. Porras
    • 1
  • T. Schaetz
    • 1
  1. 1.Max Planck Institute of Quantum OpticsGarchingGermany

Personalised recommendations