On the impossibility of a quantum sieve algorithm for graph isomorphism
Cristopher Moore, Alexander C. Russell, Piotr Śniady · 2007
It is known that any quantum algorithm for Graph Isomorphism thatworks within the framework of the hidden subgroup problem (HSP) must performhighly entangled measurements across Ω(n log n) coset states. One ofthe only known models for how such a measurement could be carried outefficiently is Kuperberg's algorithm for the HSP in the dihedral group, in whichquantum states are adaptively combined and measured according to thedecomposition of tensor products into irreducible representations. This "quantum sieve" starts with coset states, and works its way down towardsrepresentations whose probabilities differ depending on, for example, whetherthe hidden subgroup is trivial or nontrivial.