Bratteli Diagrams and Subexponential Time Quantum Algorithms for Hidden Subgroup Problems: or, Fourier Sampling Strikes Back
Cristopher Moore, Alexander C. Russell · arXiv (Cornell University) · 2005
We present an explicit measurement in the Fourier basis that solves an important case of the Hidden Subgroup Problem, including the case to which Graph Isomorphism reduces. This entangled measurement uses $k=\log_2 |G|$ registers, and each of the $2^k$ subsets of the registers contributes some information. While this does not, in general, yield an efficient algorithm, it generalizes the relationship between Subset Sum and the HSP in the dihedral group, and sheds some light on how quantum algorithms for Graph Isomorphism might work.