In 2012, I proposed the term “quantum supremacy” to describe the point where quantum computers can do things that classical computers can’t, regardless of whether those tasks are useful. ...This is funny. A few years ago, supremacy might have invoked thoughts of kings, empires, popes, and laws, but not white people. Now rationalist internet forums get frequented by misogynists and white nationalists. Preskill seems to be referring to this gripe about white supremacy.
The words “quantum supremacy” — if not the concept — proved to be controversial for two reasons. One is that supremacy, through its association with white supremacy, evokes a repugnant political stance. The other reason is that the word exacerbates the already overhyped reporting on the status of quantum technology.
The catch, as the Google team acknowledges, is that the problem their machine solved with astounding speed was carefully chosen just for the purpose of demonstrating the quantum computer’s superiority. It is not otherwise a problem of much practical interest. In brief, the quantum computer executed a randomly chosen sequence of instructions, and then all the qubits were measured to produce an output bit string. This quantum computation has very little structure, which makes it harder for the classical computer to keep up, but also means that the answer is not very informative.The term "quantum supremacy" suggests a major accomplishment. But all we really know is that the hardware is working.
However, the demonstration is still significant. By checking that the output of their quantum computer agrees with the output of a classical supercomputer (in cases where it doesn’t take thousands of years), the team has verified that they understand their device and that it performs as it should. Now that we know the hardware is working, we can begin the search for more useful applications.
We also know that they did a quantum experiment that is hard to simulate. But so what? The weather is hard to simulate. A lot of things are hard to simulate.
Here is Preskill's 2012 paper on quantum supremacy, and 2018 paper on NISQ. The latter says:
I’ve already emphasized repeatedly that it will probably be a long time before we have fault-tolerant quantum computers solving hard problems. ...So a quantum computer that tells us something we didn't already know is decades away. Or impossible.
Nevertheless, solving really hard problems (like factoring numbers which are thousands of bits long) using fault-tolerant quantum computing is not likely to happen for a while, because of the large number of physical qubits needed. To run algorithms involving thousands of protected qubits we’ll need a number of physical qubits which is in the millions, or more .