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Trapped Ion Quantum Computing
Quantum algorithms for hidden nonlinear structures
arXiv
Authors: Andrew M. Childs, Leonard J. Schulman, Umesh V. Vazirani
Year
2007
Paper ID
50222
Status
Preprint
Abstract Read
~2 min
Abstract Words
83
Citations
N/A
Abstract
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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- This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
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- Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central...
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