On the impossibility of a quantum sieve algorithm for graph isomorphism: unconditional results
Cristopher Moore; Alexander Russell; Piotr Sniady · 2006 · arXiv
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Abstract (excerpt)
It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across Ω(n \log n) coset states. One of the only known models for how such a measurement could be carried out efficiently is Kuperberg's algorithm for the HSP in the dihedral group, in which quantum states are adaptively combined and measured according to the decomposition of tensor products into irreducible representations. This ``quantum sieve'' starts with coset states, and works its way down towards representations whos
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Metadata source: arXiv