"Quantum supremacy" is a technical term that simply means demonstrating that a quantum computer can in fact perform some computation (something artificial like sampling from a certain kind of distribution) faster than a classical computer, not that the computation is useful for anything rightaway. This has not been achieved so far, but is expected to be around the corner. See this article from July: https://www.quantamagazine.org/quantum-supremacy-is-coming-h... and some of the better-informed comments on these other threads: https://news.ycombinator.com/item?id=21047804https://news.ycombinator.com/item?id=21043659