Super-computer trounced by human brain
IBM's Blue Gene super-computer has performed a record 280.6 trillion operations per second on the industry standard LINPACK benchmark. That is more than 10^14 operations per second.
The human brain contains around 10^11 brain cells, so Blue Gene could in principle deploy about 10^3 operations per second on simulating each brain cell in a simulation of the whole brain.
However, each brain cell has a lot of biological computing machinery associated with it (e.g. its large number of synapses, the dendritic tree that connects the synapses to the cell body, the cell membrane, etc), and the time scale for brain cell dynamics is around a millisecond, so the 10^3 operations per brain cell per second that Blue Gene gives you isn't anywhere near enough compute power for a real-time simulation of the brain.
If each brain cell (including all of its biological computing machinery) needs around 10^9 operations per second (1 per millisecond, times a conservative 10^6 to account for all the large number of synapses and the dendritic tree) , then the total number of operations per second that are needed for the whole brain is around 10^20 (10^9 operations per brain cell, times 10^11 brain cells).
Thus, conservatively 10^20 operations per second are needed for a real-time simulation of the human brain, but Blue Gene can supply only 10^14 operations per second. There is rather a large shortfall.
Clearly, we are nowhere near being able to simulate all of the neurons in the human brain in real time. Even if Blue Gene was fast enough, it would still lose out in terms of processing power per cubic millimetre. Blue Gene occupies a very large room (think "supermarket", or have a look at the photo here), whereas the human brain occupies a cranium.
And don't even think about comparing the relative energy requirements of Blue Gene and the human brain.
Blue Gene achieves its speed by connecting together a large number of conventional microcomputers, each of which uses a variant of a more-or-less standard computer architecture (the so-called von Neumann architecture). In the other hand, the human brain does not use anything remotely like this approach to the problem of doing computations. In effect, it uses special purpose biological hardware for each and every processing node (i.e. each brain cell plus its associated machinery), and this biological hardware operates as a fine-grained parallel computer.
To compete with a human brain, a remote descendent of Blue Gene will have to operate in a similarly fine-grained parallel way, and will thus have to be built using a much less clunky technology than tens of thousands of interconnected microcomputers.
I believe that the solution to this problem will emerge from nanotechnology, and it will use something analogous to artificial DNA to orchestrate the building of fine-grained parallel computers.