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Quantum Algorithms

Invited Talk
  • Umesh Vazirani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2286)

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).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Umesh Vazirani
    • 1
  1. 1.University of CaliforniBerkeleyUSA

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