Quantum algorithms for algebraic problems
Abstract
Quantum computers can execute algorithms that dramatically outperform classical computation. As the bestknown 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 largescale 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.
 Publication:

Reviews of Modern Physics
 Pub Date:
 January 2010
 DOI:
 10.1103/RevModPhys.82.1
 Bibcode:
 2010RvMP...82....1C
 Keywords:

 03.67.Lx;
 Quantum computation