We can prove that quantum computers are faster than classical computers at solving certain problems (like simulating atom interactions). Although IBM recently moved that goal post, and proved that we can simulate 56-qubit (and probably a little more than that) with classical supercomputers.
It's debatable how generic this 56-qubit simulation is. We can already "simulate" millions of qubits, with entanglement, as long as they dance in a particular way...
I figured as much. So whoever develops a 50-qubit quantum computer first (Google?) will have to prove that the same simulation can't be done with a supercomputer. And they'd need to be serious about it and use the latest research in classical simulation, including IBM's 56-qubit research to try and do it on a supercomputer.
Otherwise, they may claim "quantum supremacy" and 3 months later someone else will prove that the same simulation can be done on a classical computer.
