This work introduces two decision problems, StabilizerD and Orbit CosetD, and gives quantum reductions from them to the problem Orbit Superposition (Friedl et al., 2003), as well a...
It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by...
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodi...
We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is a solution to the Unique Shortest Vector Problem (SVP) under ...