The simplest quantum algorithm shows an exponential speedup over the best classical solution, this, of course, is the toy example often used in QC texts of determining whether or not a function is constant or balanced(Deutsch).
But, as John Preskill points out...this is not even the really interesting thing here. Quantum simulation actually lies outside the class of NP, because there is no efficient way to verify the solution of such a simulation.
This area is where quantum computers, in my opinion, are the most interesting, we will be able to do things we simply cannot on a classical computer....and for the record..most people commenting should know that D-WAVE operates using the Adiabatic model, and is not a universal quantum computer.
But, as John Preskill points out...this is not even the really interesting thing here. Quantum simulation actually lies outside the class of NP, because there is no efficient way to verify the solution of such a simulation.
This area is where quantum computers, in my opinion, are the most interesting, we will be able to do things we simply cannot on a classical computer....and for the record..most people commenting should know that D-WAVE operates using the Adiabatic model, and is not a universal quantum computer.