Quantum algorithms for hidden nonlinear structures

Details Quantum algorithms for hidden nonlinear structures Quantum algorithms for hidden nonlinear structures

2007-05-21

arxiv.org/abs/0705.2784v1

Proc. 48th IEEE Symposium on Foundations of Computer Science (FOCS 2007), pp. 395-404

Physics

Quantum Physics

13 pages

Scientific paper

10.1109/FOCS.2007.18

Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an alternative generalization, namely to problems of finding hidden nonlinear structures over finite fields. We give examples of two such problems that can be solved efficiently by a quantum computer, but not by a classical computer. We also give some positive results on the quantum query complexity of finding hidden nonlinear structures.

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