Editing Quantum algorithm (section)

===Hidden subgroup problem===
The [[Abelian group|abelian]] [[hidden subgroup problem]] is a generalization of many problems that can be solved by a quantum computer, such as Simon's problem, solving [[Pell's equation]], testing the [[principal ideal]] of a [[ring (mathematics)|ring]] R and [[integer factorization|factoring]]. There are efficient quantum algorithms known for the Abelian hidden subgroup problem.<ref>{{cite conference
 |last1=Boneh |first1=D.
 |last2=Lipton |first2=R. J.
 |year=1995
 |title=Quantum cryptoanalysis of hidden linear functions
 |editor-last=Coppersmith |editor-first=D.
 |book-title=Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
 |pages=424–437
 |publisher=[[Springer-Verlag]]
 |isbn=3-540-60221-6
}}</ref> The more general hidden subgroup problem, where the group is not necessarily abelian, is a generalization of the previously mentioned problems, as well as [[graph isomorphism]] and certain [[lattice problems]]. Efficient quantum algorithms are known for certain non-abelian groups. However, no efficient algorithms are known for the [[symmetric group]], which would give an efficient algorithm for graph isomorphism<ref>{{cite arXiv
 |last1=Moore |first1=C.|author1-link=Cris Moore
 |last2=Russell |first2=A.
 |last3=Schulman |first3=L. J.
 |year=2005
 |title=The Symmetric Group Defies Strong Fourier Sampling: Part I
 |eprint=quant-ph/0501056
}}</ref> and the [[dihedral group]], which would solve certain lattice problems.<ref>{{cite arXiv
 | last = Regev | first = O.
 | date = 2003
 | title = Quantum Computation and Lattice Problems
 | eprint = cs/0304005
}}</ref>