Skip to main content
SpringerLink
Log in

Programmable Quantum Processors

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We develop a mathematical description for these devices. We generalize the concept of quantum programmable processors and we propose programmable measurement devices.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lloyd S., Viola L, (2002). Phys. Rev. A, 65, 010101

    Article  MathSciNet  ADS  Google Scholar 

  2. See for example: M. A. Nielsen and I.Chuang L, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

  3. Harel G., Akulin V.M, (1999). Phys. Rev. Lett. 82, 1

    Article  ADS  Google Scholar 

  4. Brion E, Akulin V.M, Comparat D, Dumer I, Gershkovich V, Harel G, Kurizki G, Mazets I, Pillet P, Non-Holonomic Control I. arXiv: quant-ph/0507156 (2005).

  5. Lloyd S., Braunstein S.M, (1999). Phys. Rev. Lett. 82: 1784

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Hladký B., Drobný G., Bužek V., (2000). Phys. Rev. A 61, 0221202

    Article  Google Scholar 

  7. Nielsen M.A., Chuang I.L, (1997). Phys. Rev. Lett. 79, 321

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Hillery M, Bužek V., Ziman M, (2001). Fortschr. Phys 49, 987

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Hillery M, Ziman M, Bužek V., (2002). Phys. Rev. A 66, 042302

    Article  ADS  Google Scholar 

  10. Preskill J, (1998). Proc. Roy. Soc. Lond A 454, 385

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Vidal G, Masanes L, Cirac J.I, (2002). Phys. Rev. Lett. 88, 047905

    Article  ADS  Google Scholar 

  12. Hillery M, Bužek V., Ziman M, (2002). Phys. Rev. A 65, 022301

    Article  MathSciNet  ADS  Google Scholar 

  13. Helstrom C.W., (1976). Quantum Detection and Estimation Theory. Academic Press, New York

    Google Scholar 

  14. Holevo A.S., (1982). Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam

    MATH  Google Scholar 

  15. Peres A., (1993). Quantum Theory: Concepts and Methods. Kluwer, Dordrecht

    MATH  Google Scholar 

  16. Busch P, Lahti P, Mittalstead P, (1996). Quantum Theory of Measurement. Springer, Berlin

    MATH  Google Scholar 

  17. Massar S., Popescu S, (1995). Phys. Rev. Lett. 74: 1259

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Derka R, Bužek V., Ekert A.K, (1998). Phys. Rev. Lett. 80: 1571

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. Huelga S.F, Vaccaro J.A, Chefles A, (2001). Phys. Rev. A 63, 042303

    Article  ADS  Google Scholar 

  20. Preskill J,Quantum Theory of Information and Computation, see http://www. .caltech.edu/people/ preskill.

  21. Uhlmann A, Rep. Math. Phys. 9, 273 (1976); ibid 24, 229 (1986).

  22. Scarani V, Ziman M, Štelmachovič P., Gisin N, Bužek V., (2002). Phys. Rev. Lett. 88, 097905

    Article  ADS  Google Scholar 

  23. Ziman M, Štelmachovič P., Bužek V., Hillery M, Scarani V, Gisin N, (2002). Phys. Rev. A 65, 042105

    Article  ADS  Google Scholar 

  24. Braunstein S, Bužek V., Hillery M, (2001). Phys. Rev. A 63, 052313

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  26. Bužek V., Braunstein S, Hillery M, Bruß D., (1997). Phys. Rev. A 56: 3446

    Article  ADS  Google Scholar 

  27. Alber G, Delgado A, Gisin N, Jex I, Los Alamos arXive quant-ph/0008022.

  28. Bužek V., Wilson-Gordon A.D., Knight P.L., Lai W.K, (1992). Phys. Rev. A 45: 8079

    Article  ADS  Google Scholar 

  29. Pegg D.T., Barnett S.M, Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989); Pegg D.T, Vaccaro J.A, and S. Barnett M, J. Mod. Opt. 37, 1703 (1990).

  30. Wootters W.K, (1987). Ann. Phys 176: 1

    Article  MathSciNet  ADS  Google Scholar 

  31. Opatrný T., Bužek V., Bajer J, Drobný G., (1995). Phys. Rev. A 52: 2419

    Article  ADS  Google Scholar 

  32. Leonhardt U, (1995). Phys. Rev. Lett 74: 4101

    Article  MATH  MathSciNet  ADS  Google Scholar 

  33. Koniorczyk M, Bužek V., Janszky J, (2001). Phys. Rev. A 64, 034301

    Article  ADS  Google Scholar 

  34. Paz J.P, (2002). Phys. Rev. A 65, 062311

    Article  MathSciNet  ADS  Google Scholar 

  35. Galetti D., de Toledo Piza A.F.R., (1988). Physica 149A: 267

    ADS  Google Scholar 

  36. Bužek V., Keitel C.H, Knight P.L, (1995). Phys Rev A 51: 2575

    Article  ADS  Google Scholar 

  37. Alber G, Delgado A, Gisin N, Jex I, (2001). J. Phys. A 34, 8821

    Article  MATH  MathSciNet  ADS  Google Scholar 

  38. Vedral V, Barenco A, Ekert A, (1996). Phys. Rev. A 54, 147

    Article  MathSciNet  ADS  Google Scholar 

  39. Pittenger A.D, (2000). An Introduction to Quantum Computing. Birkhäuser, Boston

    MATH  Google Scholar 

  40. Fivel D.I, (1995). Phys. Rev. Lett. 74: 835

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. Ziman M., Bužek V., (2003). Int. J. Quant. Inf., 1: 527

    Article  MATH  Google Scholar 

  42. Hillery M, Ziman M, Bužek V., (2004). Phys. Rev. A 69: 042311

    Article  ADS  Google Scholar 

  43. Koniorczyk M, Bužek V., Adam P, (2006). Eur. J. Phys. D 37: 275

    Article  ADS  Google Scholar 

  44. D. E. Evans Lewis J.T, Dilations of Irreversible Evolutions in Algebraic Quantum Theory, Communications of Dublin Institute of Advanced Studies, Series A (Theoretical Physics), No. 24, (DIAS, Dublin, 1977).

  45. Dušek M., Bužek V., (2002). Phys. Rev. A 66, 022112

    Article  ADS  Google Scholar 

  46. J. Fiurášek et al., Phys. Rev. Lett. 89, 190401 (2002).

  47. Fiurášek J., Dušek M., (2004). Phys. Rev. A 69, 032302

    Article  ADS  Google Scholar 

  48. Bergou J.A., Hillery M, (2005). Phys. Rev. Lett. 71, 042314

    ADS  Google Scholar 

  49. Paz J.P., Roncaglia A., (2003). Phys. Rev. A 68, 052316

    Article  ADS  Google Scholar 

  50. Ekert A.K, Alves C.M, D. Oi K.L, Horodecki M, Horodecki P, Kwek L.C, Phys. Rev. Lett. 88, 217901 (2002).

  51. D’Ariano G.M., Perinotti P, Sacchi M.F, (2004). Europhys. Lett. 65, 165

    Article  ADS  Google Scholar 

  52. G. M. D’Ariano, Perinotti P, Sacchi M.F, in Proceedings of the 8th Int. Conf. on Squeezed States and Uncertainty Relations, H. Moya-Cessa et al. (eds.) (Rinton, Princeton, 2003), p. 86.

  53. D’Ariano G.M., Perinotti P, (2004) Phys. Rev. Lett. 93, 180503

    Article  Google Scholar 

  54. Roško M., Bužek V., Chouha P.R, Hillery M, (2003). Phys. Rev. A 68, 062302

    Article  MathSciNet  ADS  Google Scholar 

  55. Renes J.M, Blume-Kohout R., Scott A.J, Caves C.M, (2004). J. Math. Phys 45: 2171

    Article  MATH  MathSciNet  ADS  Google Scholar 

  56. P. Stelmachovič, private communication.

  57. K. Wódkiewicz, Phys. Rev. Lett. 52, 1064 (1984); Phys. Lett. A 115, 304 (1986); Phys. Lett. A 129, 1 (1988).

  58. Chefles A, (2001). Contemp. Phys. 41: 401

    Article  ADS  Google Scholar 

  59. Barnett S.M, (2001). Fortschr. Phys. 49: 909

    Article  MATH  MathSciNet  ADS  Google Scholar 

  60. Ivanovic I.D, (1987). Phys. Lett. A 123: 257

    Article  MathSciNet  ADS  Google Scholar 

  61. Dieks D, (1988). Phys. Lett. A 126: 303

    Article  MathSciNet  ADS  Google Scholar 

  62. Peres A, (1988). Phys. Lett. A 128: 19

    Article  MathSciNet  ADS  Google Scholar 

  63. Jaeger G., Shimony A, (1995). Phys. Lett. A 197: 83

    Article  MATH  MathSciNet  ADS  Google Scholar 

  64. Chefles A., Barnett S.M, (1998). Phys. Lett. A 250: 223

    Article  ADS  Google Scholar 

  65. Huttner B, Muller A, Gautier J.D, Zbinden H, Gisin N, (1996). Phys. Rev. A 54: 3783

    Article  MathSciNet  ADS  Google Scholar 

  66. Bergou J.A, Hillery M, Sun Y, (2001). Fortschr. Phys 49: 915

    Article  MATH  MathSciNet  ADS  Google Scholar 

  67. Dušek M., Jahma M, Lütkenhaus N., (2000). Phys. Rev. A 62: 022306

    Article  ADS  Google Scholar 

  68. Gilchrist A, Langford N.K, Nielsen M.A, (2005). Phys. Rev. A 71, 062310

    Article  ADS  Google Scholar 

  69. Raginsky M, (2001). Phys. Lett. A 290, 11

    Article  MATH  MathSciNet  ADS  Google Scholar 

  70. Raginsky M, (2002). Phys. Rev. A 65: 032306

    Article  ADS  Google Scholar 

  71. D’Ariano G.M., Perinotti P, quant-ph/0510033.

  72. Hillery M, Ziman M, Bužek V., (2006). Phys. Rev. A 73, 022345

    Article  ADS  Google Scholar 

  73. Brazier A, Bužek V., Knight P.L, (2005). Phys. Rev. A 71, 032306

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia

    Vladimír Bužek, Mário Ziman & Marián Roško

  2. Abteilung für Quantenphysik, Universität Ulm, 89069, Ulm, Germany

    Vladimír Bužek

  3. Quniverse, Líščie údolie 116, 841 04, Bratislava, Slovakia

    Vladimír Bužek, Mário Ziman & Marián Roško

  4. Department of Physics, Hunter College of CUNY, 695 Park Avenue, New York, NY, 10021, USA

    Mark Hillery

  5. Faculty of Informatics, Masaryk University, Botanická 68a, 602 00, Brno, Czech Republic

    Mário Ziman

Authors
  1. Vladimír Bužek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark Hillery
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mário Ziman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marián Roško
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimír Bužek.

Additional information

We dedicate this paper to Anton Zeilinger on the occasion of his 60th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bužek, V., Hillery, M., Ziman, M. et al. Programmable Quantum Processors. Quantum Inf Process 5, 313–420 (2006). https://doi.org/10.1007/s11128-006-0028-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-006-0028-z

Keywords

Pacs

Search

Navigation