there is a theory by the brilliant Roger Penrose and extended by others that the brain is just not neurons but also quantum effect

which would make it impossible to emulate via current technology

excellent PBS Space Time on that

* https://www.youtube.com/watch?v=xa2Kpkksf3k

This isn't quite the question the article is asking, but if you expand it just a bit to a brain rather than a simulation of a biological brain specifically, the specification complexity of a modern AI is not that large. You can get a good idea of the foundation of the system with some 3blue1brown videos. While just watching those and deeply understanding isn't enough to score a job at a frontier AI lab, I'd expect that a lot of what the labs do is similarly not that complicated to specify... it's coming up with the ideas, tuning them, and then trying to test them at the now-staggering scale it takes to prove them out for commercial use that is most of the issue.

The complexity of the AI itself, the final weights, is vastly higher, because that incorporates all the data that was flowed through the "brain".

In a decent encoding you could probably still fit the initial state of the frontier models comfortably in just a few kilobytes of code-golfed code, including the update functions and every necessary for the actual training. Recall the specification complexity is the smallest program that can create the initial state, not the initial state itself; the specification complexity of "give me a trillion 64-bit numbers generated from this psuedo-random number generator" is on the order of that very English sentence in size, not 8 tebibytes of specification complexity.

Is the result a biological brain? Obviously not. Biological brains do not do what the LLMs are doing. But unlike someone asking this question 20 or 30 years ago, where "yeah, but what if some other architecture could work too?" was still largely hypothetical, and neural nets were still largely toys, now it isn't. We may argue if an LLM is as smart as a human but I would say that at least on its playing field it is quite clearly smarter than most biological brains in existence on most measures we care about. I have to qualify "on its playing field" because it is fundamentally a text completion engine, so for instance even very very tiny biological systems still beat it on things like "ability to drive an ant body around to do useful tasks". That's a separate field of AI right now. Stay tuned on that matter, but it's not how things work today for sure.

There is still something to what biological brains do that we are not matching; as I like to say, humans do what they do without the entire contents of the internet being poured through their head multiple times over. But the idea that maybe we don't have to exactly match biology to get something useful is no longer just a theory.