Maybe I'm missing something, but it appears to me quantum supremacy cannot be proven empirically, only theoretically. Quantum supremacy means you can prove that

Maybe I'm missing something, but it appears to me quantum supremacy cannot be proven empirically, only theoretically. Quantum supremacy means you can prove that a quantum computer performs task A faster than any classical computer could do it. Not faster than a classical computer currently does it. For example, Schor's algorithm can factorize in polynomial time and classical factorization takes superpolynomial time. The problem is that it's not easy at all to show classical factorization is superpolynomial, and some people actually think there's a high likelihood it's actually polynomial. So, quantum supremacy is pretty much theoretical CS in the area of lower bounds for classical algorithmic problems.