[krastanov]

There is no evidence that quantum annealing (what D-Wave does) is any better than classical computers.

There is a lot of evidence that quantum computers (the gate model) or, equivalently, quantum adiabatic computing is better than classical computing. All of it is based on a family of conjectures about the complexity classes P, BQP, and NP.

Scott Aaronson's blog is one of my go-to suggestions for rigorous introduction to the topic.