Abstract
We describe how physics of computation determines computational complexity. In particular we show how quantum phenomena lead to qualitatively new modes of computation. An ideal quantum computer would allow to face certain tasks out of reach of classical computers, the factorization problem being the most striking example. Experimentally, however, implementation of quantum computation faces some serious difficulties due to an interaction with the environment which causes decoherence. We mention quantum error-correction as a process which can, to some extent, protect quantum computers from unwelcome effects of dissipation and decoherence. This is a brief, introductory review of quantum computation. It is based on [1].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. Barenco and A. Ekert, Acta Physica Slovaca 45, 205–216 (1995). A. Barenco, Contemp. Phys. 37 (5), 375-389 (1996).
R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
D. Deutsch, Proc. R. Soc. London A 400, 97 (1985).
R. P. Feynmann, Int. J. Theor. Phys. 21, 467 (1982).
D. Deutsch. and R. Jozsa, Proc. R. Soc. London A 439, 553 (1992).
E. Bernstein and U. Vazirani, in Proceedings, 25th ACM Symposium on the Theory of Computation, p.11 (1993).
D. S. Simon in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, S. Goldwasser, ed. (IEEE Computer Society Press, Los Alamitos, CA), p. 116 (1994).
P. W. Shor in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, S. Goldwasser, ed. (IEEE Computer Society Press, Los Alamitos, CA), p. 124 (1994).
R. Rivest, A. Shamir, and L. Adleman, On Digital Signatures and PublicKey Cryptosystems, MIT Laboratory for Computer Science, Technical Report, MIT/LCS/TR-212 (January 1979).
R. D. Silverman, Math. Comp.. 48, 329 (1987).
A. K. Lenstra, H. W. Lenstra Jr., M. S. Manasse, and J. M. Pollard, in Proceedings, 22nd ACM Symposium on the Theory of Computing, pp.564–572 (1990).
D. Welsh Codes and Cryptography (Clarendon Press, Oxford, 1988).
C. H. Papadimitriou, Computational Complexity (Addison-Wesley, Reading, 1994).
A. S. Holevo, Problemy Peredachi Informatsii 9, 3 (1979) (this journal is translated by IEEE under the title Problems of Information Transfer).
E. B. Davies, IEEE Trans. Inform. Theory 24, 596 (1978).
C. A. Fuchs and C. M. Caves, Phys.Rev. Lett. 73, 3047 (1994).
R. Jozsa and B. Schumacher, J. Mod. Optics 41, 2343 (1994).
S. Wiesner, Sigact News 15(1), 78 (1983).
C. H. Bennett, Phys. Rev. Lett. 68 3121 (1982).
C. H. Bennett and G. Brassard, in Proceedings, IEEE international Conference on Computers, Systems, and Signal Processing, Bangalore, India 175, (IEEE, New York, 1984).
A. K. Ekert, Phys. Rev. Lett 71, 4287 (1993).
C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
C. H. Bennett, SIAM J. Comput. 18(4), 766 (1989).
M. R. Schroeder, Number Theory in Science and Communication (Springer, New York, 1984).
D. Coppersmith, IBM Research Report No. RC19642 (1994).
A. K. Ekert and R. Jozsa, Rev. Mod. Phys., to appear (1995).
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th edn. (Oxford University Press, Oxford, 1965).
D. Deutsch, Proc. R. Soc. London A 425, 73 (1989).
A. Barenco, Proc. R. Soc. London A 449, 679 (1995).
T. Sleator and H. Weinfurter, Phys. Rev. Lett. 74, 4087 (1995).
D. Deutch, A. Barenco, and A. K. Ekert, Proc. R. Soc. London A, in press (1995).
S. Lloyd, Los Alamos National Laboratory preprint (1994).
D. E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (Addison-Wesley, Reading, 1981).
M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 72, 3339 (1994).
A. Barenco, D. Deutsch, R. Jozsa, and A. Ekert, Phys. Rev. Lett. 74, 4083 (1995).
J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
Q.A. Turchette, C. J. Hood, C. J. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
W. Unruh, Phys. Rev. A 51, 992 (1994).
G. M. Palma, K. A. Suominen, and A. Ekert, Proc. R. Soc. London A 452, 567 (1996).
D. Di Vincenzo, Phys. Rev. A 50, 1015 (1995).
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1977).
R. Laflamme, C Miguel, J. P. Paz, and W. H. Zurek, Phys. Rev. Lett. 77, 198 (1996).
P. W. Shor, Phys. Rev. A 52, R2493 (1995).
P. W. Shor, quant-ph/9605011.
D. P. Di Vicenzo and P. W. Shor, Phys. Rev. Lett. 77, 3260 (1996).
A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 1098 (1996).
A. M. Steane, Proc. R. Soc. A 452, 2551 (1996).
A. Ekert and C. Macchiavello, Phys. Rev. Lett. 77, 2585 (1996).
E. Knill and R. Laflamme, quant-ph/9604034.
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, quantph/9605005.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Barenco, A., Huelga, S.F., Ekert, A.K. (1997). Quantum Computation. In: Ferrero, M., van der Merwe, A. (eds) New Developments on Fundamental Problems in Quantum Physics. Fundamental Theories of Physics, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5886-2_6
Download citation
DOI: https://doi.org/10.1007/978-94-011-5886-2_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6487-3
Online ISBN: 978-94-011-5886-2
eBook Packages: Springer Book Archive