Joe Carlsmith with a really detailed report on computational upper bounds and lower bounds on simulating a human brain: 

Open Philanthropy is interested in when AI systems will be able to perform various tasks that humans can perform (“AI timelines”). To inform our thinking, I investigated what evidence the human brain provides about the computational power sufficient to match its capabilities. This is the full report on what I learned. A medium-depth summary is available here. The executive summary below gives a shorter overview.

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Let’s grant that in principle, sufficiently powerful computers can perform any cognitive task that the human brain can. How powerful is sufficiently powerful? I investigated what we can learn from the brain about this. I consulted with more than 30 experts, and considered four methods of generating estimates, focusing on floating point operations per second (FLOP/s) as a metric of computational power.

These methods were:

1. Estimate the FLOP/s required to model the brain’s mechanisms at a level of detail adequate to replicate task-performance (the “mechanistic method”).1
2. Identify a portion of the brain whose function we can already approximate with artificial systems, and then scale up to a FLOP/s estimate for the whole brain (the “functional method”).
3. Use the brain’s energy budget, together with physical limits set by Landauer’s principle, to upper-bound required FLOP/s (the “limit method”).
4. Use the communication bandwidth in the brain as evidence about its computational capacity (the “communication method”). I discuss this method only briefly.

None of these methods are direct guides to the minimum possible FLOP/s budget, as the most efficient ways of performing tasks need not resemble the brain’s ways, or those of current artificial systems. But if sound, these methods would provide evidence that certain budgets are, at least, big enough (if you had the right software, which may be very hard to create – see discussion in section 1.3).2

Here are some of the numbers these methods produce, plotted alongside the FLOP/s capacity of some current computers.

These numbers should be held lightly. They are back-of-the-envelope calculations, offered alongside initial discussion of complications and objections. The science here is very far from settled.