Quantum Supremacy Task

I’m trying to understand the task performed by Google’s Sycamore that recently achieved alleged Quantum Supremacy. I’ve read the paper in Nature but the actual task that would have taken 10,000 years to compete is over my head. Is anyone able to explain it in simpler terms?

First of all it seems that google has exaggerated a little bit by shooting the $10000$ years results. It seems that IBM, on his current and most powerful classic super computer, is able to perform the same task in $2.5$ days, saving the entire search space (Hilbert space) on a $250$ petabytes hard drive. This does not mean that google's result is not to be taken into consideration: it is definitely a milestone but it will not change the world as many claim, it will not provide us with stable and multipurpose quantum computers within a year or two (
to tell the truth, with current technologies it is not even practically possible to get computers with enough qbits and keep them in a consistent state).

Having made this premise, we come to the experiment:

Essentially (and in simple terms, very simple terms)
what they did was to correctly sample from the possible outputs of a $53$ qbits random quantum circuit using a statistical test called linear cross-entropy benchmark and sampling about $5000000$ results in about $200$ seconds. The test was a stochastic triumph.

Some notes:

• people (outside the discipline) are going crazy blathering of a proof of $P = NP$ or $BQP = BPP$ and then some...

All these things are false, none of these important open problems have been solved by the experiment.

• The real importance of having scalable quantum computers lies in being able to perform simulations of physical systems efficiently, which entails dramatic results in the industrial field: desig of new medicines, design of new materials, etc.

• Quantum computers will not spell the end of cryptography: not all cryptographic methods can be efficiently cracked by a quantum computation and, in addition, we already know post-quantum cryptographic techniques: for example lattice cryptography.

StackExchange Computer Science Q#116244, answer score: 19