Skip to main content
Log in

Quantum computing with mixed states

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no efficient classical algorithms are known. We suggest a new implementation of quantum computation with initially mixed states in which an algorithm realization is achieved by means of optimal basis independent transformations of qubits.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Jozsa, N. Linden, Proc. Soc. Lond. A 459, 2011 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. R. Blume-Kohout, C.M. Caves, I.H. Deutsch, Found. Phys. 32, 1641 (2002)

    Article  MathSciNet  Google Scholar 

  3. N. Linden, S. Popescu, Phys. Rev. Lett. 87, 047901 (2001)

    Article  ADS  Google Scholar 

  4. S.L. Braunstein, A.K. Pati, Quantum Inf. Comput. 2, 399 (2002)

    MathSciNet  MATH  Google Scholar 

  5. E. Biham, G. Brassard, D. Kenigsberg, T. Mor, Theor. Comput. Sci. 320, 15 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. D.P. DiVincenzo, Fortschr. Phys. 48, 771 (2000)

    Article  MATH  Google Scholar 

  8. J.I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 4091 (1995)

    Article  ADS  Google Scholar 

  9. T. Pelizzari, S.A. Gardiner, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 75, 3788 (1995)

    Article  ADS  Google Scholar 

  10. N.A. Gershenfeld, I.L. Chuang, Science 275, 350 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. E. Knill, R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)

    Article  ADS  Google Scholar 

  12. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

  13. D.P. DiVincenzo, Phys. Rev. A 51, 1015 (1995)

    Article  ADS  Google Scholar 

  14. V. Scarani, S. Iblisdir, N. Gisin, A. Acin, Rev. Mod. Phys. 77 1225 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. P. Shor, Proc. of the 35th Ann. Symp. of the Found. of Comp. Sci. (1994), p. 124

  16. L.K. Grover, Phys. Rev. Lett. 79, 325 (1997)

    Article  ADS  Google Scholar 

  17. D. Deutsch, R. Jozsa, Proc. R. Soc. Lond. A 439, 553 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. D.R. Simon, SIAM J. Comput. 26, 1474 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. G.M. Palma, K.-A. Suominen, A.K. Ekert, Proc. R. Soc. Lond. A 452, 567 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. D.J. Shepherd, arXiv:1005.1425v1

  21. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  22. V. Bužek, M. Hillery, R.F. Werner, Phys. Rev. A 60, R2626 (1999)

    Article  ADS  Google Scholar 

  23. N. Gisin, S. Popescu, Phys. Rev. Lett. 83, 432 (1999)

    Article  ADS  Google Scholar 

  24. A.K. Pati, Phys. Rev. A 66, 062319 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  25. M. Siomau, S. Fritzsche, Eur. Phys. J. D 60, 417 (2010)

    Article  ADS  Google Scholar 

  26. A.K. Pati, Phys. Rev. A 63, 014302 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  27. W.K. Wootters, W.H. Zurek, Nature 299, 802 (1982)

    Article  ADS  Google Scholar 

  28. V. Bužek, M. Hillery, Phys. Rev. A 54, 1844 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  29. D. Bruß, M. Cinchetti, G.M. DAriano, C. Macchiavello, Phys. Rev. A 62, 012302 (2000)

    Article  ADS  Google Scholar 

  30. R.F. Werner, Phys. Rev. A 58, 1827 (1998)

    Article  ADS  Google Scholar 

  31. J. Fiurášek, Phys. Rev. A 67, 052314 (2003)

    Article  ADS  Google Scholar 

  32. M. Siomau, S. Fritzsche, Eur. Phys. J. D 57, 293 (2010)

    Article  ADS  Google Scholar 

  33. G.-F. Dang, H. Fan, Phys. Rev. A 76, 022323 (2007)

    Article  ADS  Google Scholar 

  34. C.-S. Niu, R.B. Griffiths, Phys. Rev. A 60, 2764 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  35. L.-M. Duan, G.-C. Guo, Phys. Rev. Lett. 80, 4999 (1998)

    Article  ADS  Google Scholar 

  36. A.K. Pati, Phys. Rev. Lett. 83, 2849 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. D. Bruß, C. Macchiavello, Found. Phys. 33, 1617 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  38. E. Knill, R. Laflamme, G.J. Milburn, Nature 409, 46 (2001)

    Article  ADS  Google Scholar 

  39. P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowling, G.J. Milburn, Rev. Mod. Phys. 79, 135 (2007)

    Article  ADS  Google Scholar 

  40. R. Okamoto, J.L. O’Brien, H.F. Hofmann, S. Takeuchi, arXiv:1006.4743v1

  41. H. Häffner, C.F. Roos, R. Blatt, Phys. Rep. 469, 155 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  42. J.P. Home, D. Hanneke, J.D. Jost, J.M. Amini, D. Leibfried, D.J. Wineland, Science 325, 1227 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  44. D.N. Biggerstaff, R. Kaltenbaek, D.R. Hamel, G. Weihs, T. Rudolph K.J. Resch, Phys. Rev. Lett. 103, 240504 (2009)

    Article  ADS  Google Scholar 

  45. C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, J.-W. Pan, Nature Phys. 3, 91 (2007)

    Article  ADS  Google Scholar 

  46. T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L. O’Brien, Nature 464, 45 (2010)

    Article  ADS  Google Scholar 

  47. F. DeMartini, V. Bužek, F. Sciarrino, C. Sias, Nature 419, 815 (2002)

    Article  ADS  Google Scholar 

  48. T.B. Pittman, B.C. Jacobs, J.D. Franson, Opt. Commun. 246, 545 (2005)

    Article  ADS  Google Scholar 

  49. S. Fasel, N. Gisin, G. Ribordy, V. Scarani, H. Zbinden, Phys. Rev. Lett. 89, 107901 (2002)

    Article  ADS  Google Scholar 

  50. P. Milman, H. Ollivier, J.M. Raimond, Phys. Rev. A 67, 012314 (2003)

    Article  ADS  Google Scholar 

  51. J. Yang, Y.-F. Yu, Z.-M. Zhang, S.-H. Liu, Phys. Rev. A 77, 034302 (2008)

    Article  ADS  Google Scholar 

  52. B.-L. Fang, Z. Yang, L. Ye, Phys. Rev. A 79, 054308 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Siomau.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Siomau, M., Fritzsche, S. Quantum computing with mixed states. Eur. Phys. J. D 62, 449–456 (2011). https://doi.org/10.1140/epjd/e2011-20070-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjd/e2011-20070-y

Keywords

Navigation