Abstract: Last fall, a team at Google announced the first-ever demonstration of “quantum computational supremacy”—that is, a clear quantum speedup over a classical computer for some task—using a 53-qubit programmable superconducting chip called Sycamore. Google’s accomplishment drew on a decade of research in my field of quantum complexity theory. This talk will discuss questions like: what exactly was the (contrived) problem that Sycamore solved? How does one verify the outputs using a classical computer? And how confident are we that the problem is classically hard—especially in light of subsequent counterclaims by IBM and others? I’ll end with a possible application that I’ve been developing for Google’s experiment: namely, the generation of trusted public random bits, for use (for example) in cryptocurrencies.