Abstract
Quantum computers are the only model of computing to credibly violate the modified Church-Turing thesis, which states that any reasonable model of com-putation can be simulated by a probabilistic Turing Machine with at most poly-nomial factor simulation overhead. This is dramatically demonstrated by Shor’s polynomial time algorithms for factorization and discrete logarithms [13]. Shor’s algorithm, as well as the earlier algorithm due to Simon [12] can both be cast into the general framework of the hidden subgroup problem (see for example [10]). Two recent papers [11],[9] study how well this framework extends to solving the hidden subgroup problem for non-abelian groups (which includes the graph iso-morphism problem).
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
Bernstein E and Vazirani U, 1993, Quantum complexity theory, SIAM Journal of Computation 26 5 pp 1411–1473 October, 1997.
Bennett, C.H., Bernstein, E., Brassard, G. and Vazirani, U.,“Strengths and weaknesses of quantum computation,”SIAM J.Computing, 26, pp.1510–1523 (1997).
van Dam, W., Hallgren, H.,“Efficient Quantum Algorithms for Shifted Quadratic Character Problems ”, quant-ph/0011067.
van Dam, W., Mosca, M., Vazirani, U.,“How Powerful is Adiabatic Quantum Computing?”FOCS,2001.
van Dam, W., Vazirani, U.,“On the Power of Adiabatic Quantum Computing” manuscript, 2001.
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser,“Quantum Comput tion by Adiab tic Evolution ”, quant-ph report no. 0001106 (2000)
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda,“A Quantum Adiabatic Evolution Algorithm Applied to Random Inst nces of an NP-Complete Problem”, Science, Vol.292, April, pp.472–476 (2001)
Grover, L.,“Quantum mechanics helps in searching for needle in haystack,” Phys.Rev.Letters, 78, pp.325–328 (1997).
Grigni, M., Schulman, S., Vazirani, M., Vazirani, U.,“Quantum Mech nical Al-gorithms for the Non beli n Hidden Subgroup Problem”, In Proceedings of the Thirty-third Annual ACM Symposium on the Theory of Computing Crete, Greece, 2001.
L. Hales and S. Hallgren.Quantum Fourier S mpling Simplified. In Proceedings of the Thirty-first Annual ACM Symposium on the Theory of Computing pages 330–338,Atlanta,Georgia, 1–4 May 1999.
Hallgren, S., Russell, A., T-Shma, A.,“Normal subgroup reconstruction nd quantum computation using group representations ”, In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing 627–635, 2000.
D. Simon.“On the power of quantum comput tion.” In Proc. 35th Symposium on Foundations of Computer Science (FOCS), 1994.
Shor P W, Polynomial-time lgorithms for prime factorization and discrete logarithms on quantum computer, SIAM J. Comp., 26 No.5, pp 1484–1509, October 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vazirani, U. (2002). Quantum Algorithms. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_5
Download citation
DOI: https://doi.org/10.1007/3-540-45995-2_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43400-9
Online ISBN: 978-3-540-45995-8
eBook Packages: Springer Book Archive