Quantum algorithms for algebraic problems

Details Quantum algorithms for algebraic problems Quantum algorithms for algebraic problems

2008-12-02

arxiv.org/abs/0812.0380v1

Reviews of Modern Physics 82, 1-52 (2010)

Physics

Quantum Physics

52 pages, 3 figures, to appear in Reviews of Modern Physics

Scientific paper

10.1103/RevModPhys.82.1

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 large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor.

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