Quantum algorithms for algebraic problems

@article{Childs2008QuantumAF,
  title={Quantum algorithms for algebraic problems},
  author={Andrew M. Childs and Wim van Dam},
  journal={Reviews of Modern Physics},
  year={2008},
  volume={82},
  pages={1-52}
}
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a… 

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