Abstract
The quantum factorization is probably the most famous algorithm in quantum computation. The algorithm succeeds only when some random number with an even order relative to factorized composite integer is fed as the input to the quantum order finding algorithm. Moreover, post processing of the quantum measurement recovers the correct order only for some subset of possible values. It is well known that numbers with even orders are found with probability not less than 1/2. However, numerical simulation proves that probability of such event exhibits grouping on some discrete levels above that limit. Thus, one may conclude that usage of the lowest estimate leads to underestimation of the successful factorization probability. The understanding of the observed grouping requires further research in that field.
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.
References
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci. Comput. 26, 1484–1509 (1997)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: 28th Annual ACM Symposium on the Theory of Computing, pp. 212–219 (1996)
Gerjuoy, E.: Shor’s factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers. A. J. Phys. 73, 521–540 (2005)
Knill, E.: On Shor’s quantum factor finding algorithm: Increasing the probability of success and tradeoffs involving the Fourier Transform modulus, Technical Report LAUR-95-3350, Los Alamos Laboratory (1995), http://www.eskimo.com/~knill/cv/reprints/knill:qc1995c.ps
McAnally, D.: A refinement of Shor’s algorithm (2001), http://xxx.lanl.gov/pdf/quant-ph/0112055
Bourdon, P.S., Williams, H.T.: Probability estimates for Shor’s algorithm. Quant. Inf. Comput. 7, 522–550 (2007)
Ekert, A., Jozsa, R.: Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys. 68, 733–753 (1996)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Desurvire, E.: Classical and Quantum Information Theory. Cambridge University Press, Cambridge (2009)
Vandersypen, L.M.K., Steffen, M., Breyta, G., Yannoni, C.S., Sherwood, M.H., Chuang, I.L.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Zawadzki, P. (2009). A Numerical Simulation of Quantum Factorization Success Probability. In: Tkacz, E., Kapczynski, A. (eds) Internet – Technical Development and Applications. Advances in Intelligent and Soft Computing, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05019-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-05019-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05018-3
Online ISBN: 978-3-642-05019-0
eBook Packages: EngineeringEngineering (R0)