TY - JOUR
T1 - Quantum algorithms for hidden nonlinear structures
Y1 - 2007
A1 - Andrew M. Childs
A1 - Leonard J. Schulman
A1 - Umesh V. Vazirani
AB - 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.
UR - http://arxiv.org/abs/0705.2784v1
J1 - Proc. 48th IEEE Symposium on Foundations of Computer Science (FOCS 2007)
U5 - 10.1109/FOCS.2007.18
ER -