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 ...
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...
We show that Graph Isomorphism is in the complexity class SPP, and hence it is in ⊕P (in fact, it is in ModkP for each k ≥ 2). We derive this result as a corollary of a more g...