Computers can get quite fast.
Obviously we can make a computer faster by making it more parallel. That's exactly how GPUs run so fast. To level the playing field, we can measure speed per unit mass. This is what is done in the calculations of the Sentience Quotient. The sentient quotient measures the number of bits/s of processing power a computer has, divided by the mass of its processor (the brain, if you apply this to humans). It is typically calculated in terms of bits/s/kg, and then we drop the units and take the log-10 of that number. This final number is the SQ of a system.
By our best estimates, a human has a SQ of +13 with all other animals clustered slightly below that (they're all using neurons, so no surprise that they have similar SQ). Plants tend to score a SQ -2, while carnivorous plants reach a SQ +1.
The famous Cray-1 supercomputer had a SQ of +9, while the latest powerhouse, Watson, checks in somewhere between SQ+11 and SQ+12.
Interestingly, there are some limits to this calculation, showing the bounds of computing. At SQ-70, we have a lower limit consisting of using all of the known mass of the universe to calculate a single bit answer using all of the time left in the known universe. At SQ+50, we start running into quantum limits about how much information can actually be stored in a kilogram of matter.
Now we don't know how close to SQ+50 is actually physically possible, but the Wikipedia article linked above suggests that one known approach using Josephson junctions as switches in a computer made of superconducting materials can achieve a SQ+23. This would make it 10,000,000,000 more efficient than the human brain in terms of computation rate per unit mass!