No, quantum supremacy has been displayed already by google[0].
[0]: https://ai.googleblog.com/2019/10/quantum-supremacy-using-pr...
[0]: https://ai.googleblog.com/2019/10/quantum-supremacy-using-pr...
https://www.scottaaronson.com/blog/?p=4317
> So, tl;dr, the quantum computer is simply asked to apply a random (but known) sequence of quantum operations—not because we intrinsically care about the result, but because we’re trying to prove that it can beat a classical computer at some well-defined task.