See Scott Aaronson’s blog. It seems like researchers in John Martinis’s group at Google might have managed to demonstrate that a quantum computer can produce samples passing a certain statistical test for which we know no efficient classical algorithm to do so.
Of course I can’t help but posting again the fake nytimes headline I produced for my 2016 crypto course when I wanted to motivate the study of so called “quantum-resistant cryptography”:
Windows On Theory 
Cool, but what is your take on it? Is this (judging by the leaked, draft paper) really “quantum supremacy”?
I actually haven’t seen the leaked paper – is it available? I do trust Aaronson as an expert on this matter