Abstract
In this chapter, the Shor’s quantum algorithm for factoring integers is described. Factoring integers plays an important role in modern cryptography. We start by reviewing some fundamental facts of number theory.
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
References
Ekert, A., Jozsa, R.: Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys. 68, 733–753 (1996)
Iriyama, S., Ohya, M.: Review on quantum chaos algorithm and generalized quantum Turing machine. In: QP-PQ: Quantum Prob. White Noise Anal., Quantum Bio-Informatics, vol. 21, pp. 126–141. World Scientific, Singapore (2008)
Shor, P.W.: Algorithms for quantum computations: discrete logarithms and factoring. In: Proc. of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE Comput. Soc., Los Alamitos (1994)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484 (1997)
Vinogradov, I.M.: Basics of Number Theory. Nauka, Moscow (1963)
Volovich, I.V.: Quantum computing and Shor’s factoring algorithm. quant-ph/0109004 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Ohya, M., Volovich, I. (2011). Quantum Algorithms II. In: Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems. Theoretical and Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0171-7_13
Download citation
DOI: https://doi.org/10.1007/978-94-007-0171-7_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0170-0
Online ISBN: 978-94-007-0171-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)