We don't have a theoretical proof of a superpolynomial speedup on your favorite problem, no. But as a dear friend and colleague is fond of saying, "it works in

We don't have a theoretical proof of a superpolynomial speedup on your favorite problem, no. But as a dear friend and colleague is fond of saying, "it works in theory -- but does it work in practice?" Not your favorite problem; but one capability we've added recently is the ability to sample Ising problems with a nonzero transverse field. I'm yet unaware of a classical algorithm that can efficiently approximate this problem, though that isn't a hot research problem at the moment. The "of a quantum nature" question has been affirmed rather conclusively. Our qubits are capable of entanglement and cotunelling (you may recall a "billion times speedup" result which got way overhyped -- the actual nugget there was a demonstration that groups of 8 qubits could cotunnel to find solutions that were "hidden" from general-purpose Ising solvers), and for example, when we simulate materials which should exhibit quantum properties, we see those properties emerge without any sort of "fine tuning" aside from compensation for known irregularities.