Quantum Algorithms to Solve the Hidden Shift Problem for Quadratics and for Functions of Large Gowers Norm

@article{Rtteler2009QuantumAT,
  title={Quantum Algorithms to Solve the Hidden Shift Problem for Quadratics and for Functions of Large Gowers Norm},
  author={Martin R{\"o}tteler},
  journal={ArXiv},
  year={2009},
  volume={abs/0911.4724}
}
  • M. Rötteler
  • Published 20 August 2009
  • Computer Science, Mathematics
  • ArXiv
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular exponentiation function. In a generalization of this idea, quantum Fourier sampling can be used to discover hidden subgroup structures of some functions much more efficiently than it is possible classically. Another problem for which the Fourier transform has… 
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