Details: The authors of the theoretical proof, published today in Science, showed that quantum computers can solve some problems faster than conventional machines.

A classical computer — the field’s word for the computers we use today — would need to be impossibly powerful to solve these increasingly difficult problems.

Until now, the biggest hint of a quantum advantage has been that for some problems, the best quantum algorithms that have been discovered are faster than the best classical algorithms discovered so far.

That was a pretty big hint, but not proof.