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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 90))

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Abstract

As simulation techniques are maturing, new connection between previously separate fields appear. We present numerical simulations on the quantum dimer model. They show that this model, originally derived as effective model for the low-energy physics of frustrated Ising models, has the right properties to be used in a physical realization of topologically protected quantum bits. A topologically protected quantum bit has the advantage of being passively stable against decoherence and thus does not require error correction schemes

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References

  1. A.Yu. Kitaev: Fault-tolerant quantum computation by anyons. Report quant-ph/9707021

    Google Scholar 

  2. L. Ioffe, M.V. Feigel'man, A. Ioselevich, D. Ivanov, M. Troyer and G. Blatter: Nature 415, 507 (2002)

    Article  Google Scholar 

  3. J.I. Cirac and P. Zoller: Phys. Rev. Lett. 74, 4091 (1995)

    Article  ADS  Google Scholar 

  4. C. Monroe, D. Meekhof, B. King, W. Itano and D. Wineland: Phys. Rev. Lett. 75, 4714 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Q. Turchette, C. Hood, W. Lange, H. Mabushi, and H.J. Kimble: Phys. Rev. Lett. 75, 4710 (1995)

    Article  ADS  Google Scholar 

  6. D. Loss and D.P. DiVincenzo: Phys. Rev. A 57, 120 (1998)

    Article  ADS  Google Scholar 

  7. A. Shnirman, G. Schön, and Z. Hermon: Phys. Rev. Lett. 79, 2371 (1997)

    Article  ADS  Google Scholar 

  8. D.V. Averin: Solid State Commun. 105, 659 (1998)

    Article  ADS  Google Scholar 

  9. J.E. Mooij, T.P. Orlando, L.S. Levitov, L. Tian, C.H. van der Wal, C.H. and S. Lloyd: Science 235, 1036 (1999)

    Article  Google Scholar 

  10. L. Ioffe, V.B. Geshkenbein, M.V. Feigel’man, A.L. Fauchère and G. Blatter: Nature 398, 678 (1999)

    Article  ADS  Google Scholar 

  11. Y. Nakamura, Yu.A. Pashkin and J.S. Tsai: Nature 398, 786–788 (1999)

    Article  ADS  Google Scholar 

  12. J.R. Friedman, V. Patel, W. Chen, S.K. Tolpygo and J.E. Lukens: Nature 406, 43 (2000)

    Article  ADS  Google Scholar 

  13. C.H. van der Wal, A.C.J. ter Haar, F.K. Wilhelm, R.N. Schouten, C.J.P.M. Harmans, T.P. Orlando, S. Lloyd, and J.E. Mooij: Science 290, 773 (2000)

    Article  ADS  Google Scholar 

  14. J. Preskill: Fault-tolerant quantum computation.

    Google Scholar 

  15. Z. Bai, J. Demmel and J. Dongarra (Eds.), Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, 2000)

    Google Scholar 

  16. G.W. Stewart: Matrix Algorithms (SIAM, 2001)

    Google Scholar 

  17. R. Barret, M. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1993)

    Google Scholar 

  18. J.G. Siek, A. Lumsdaine and L.-Q. Lee, in Proceedings of the SIAM Workshop on Object Oriented Methods for Inter-operable Scientific and Engineering Computing (OO’98) (SIAM, 1998); the library is availavle on the web at: http://www.osl.iu.edu/research/itl/

  19. http://www.comp-phys.org/software/ietl/

  20. J.K. Cullum and R.A. Willoughby: J. Comput. Phys. 44, 329–358 (1981); J.K. Cullum and R.A. Willoughby: Lanczos algorithms for Large Symmetric Eigenvalue Computations. Vols. 1 and 2, Theory. (Birkhauser, Boston 1985)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. J.G. Siek and A. Lumsdaine, in Modern Software Tools for Scientific Computing (Birkhäuser, Boston 1999); the library is availavle on the web at: http://www.osl.iu.edu/research/mtl/

    Google Scholar 

  22. T. Veldhuizen, in Led. Notes in Computer Science 1505 223 (1998); the library is available on the web at http://www.oonumerics.org/blitz/

    Article  Google Scholar 

  23. M. Troyer, Ph.D. thesis (ETH Zürich, 1994)

    Google Scholar 

  24. T. Veldhuizen, C++ Report 7, 26 (1995); A.D. Robinson: Computers in Physics 10, 458 (1996)

    Google Scholar 

  25. M. Troyer: Lect. Notes in Computer Science 1732, 164 (1999)

    Article  Google Scholar 

  26. See the documentation at http://xml.comp-phys.org

  27. http://www.comp-phys.org/software/PALM++/lattice/

  28. L.Q. Lee, A. Lumsdaine and J.G. Siek: The Boost Graph Library (Addison Wesley, 2001)

    Google Scholar 

  29. R. Moessner, and S.L. Sondhi: Phys. Rev. Lett. 86, 1881 (2001)

    Article  ADS  Google Scholar 

  30. R. Moessner, and S.L. Sondhi: Phys. Rev. B 63, 224401 (2001)

    Article  ADS  Google Scholar 

  31. S.A. Kivelson, D.S. Rokhsar, and J.P. Sethna: Phys. Rev. B 35, 8865 (1987)

    Article  ADS  Google Scholar 

  32. D.S. Rokhsar, and S.A. Kivelson: Phys. Rev. Lett. 61, 2376 (1988)

    Article  ADS  Google Scholar 

  33. X.G. Wen: Phys. Rev. B 44, 2664 (1991)

    Article  ADS  Google Scholar 

  34. E. Fradkin: Field Theories of Condensed Matter Systems. (Addison Wesley, Redwood City, CA 1991)

    MATH  Google Scholar 

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Troyer, M., Ioffe, L.B., Feigel’man, M.V., Ioselevich, A., Ivanov, D., Blatter, G. (2003). From Frustrated Ising Models to Quantum Computing. In: Landau, D.P., Lewis, S.P., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics XV. Springer Proceedings in Physics, vol 90. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55522-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-55522-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62423-0

  • Online ISBN: 978-3-642-55522-0

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