The human brain contains about 100 billion neurons ($10^{11}$) and about a hundred trillion synapses ($10^{14}$). Each neuron can fire about 100 times a second. If we model the brain as a simple neural network, then it would be equivalent to a machine that requires 1016 calculations per second and 1013 bits of memory.
From Wikipedia
Kurzweil introduces the idea of "uploading" a specific brain with every mental process intact, to be instantiated on a "suitably powerful computational substrate". He writes that general modeling requires 1016 calculations per second and 1013 bits of memory, but then explains uploading requires additional detail, perhaps as many as 1019 cps and 1018 bits. Kurzweil says the technology to do this will be available by 2040.
According to this site here:
Using the NEST software framework, the team led by Markus Diesmann and Abigail Morrison succeeded in creating an artificial neural network of 1.73 billion nerve cells connected by 10.4 trillion synapses. While impressive, this is only a fraction of the neurons every human brain contains. Scientists believe we all carry 80-100 billion nerve cells
It took 40 minutes with the combined muscle of 82,944 processors in K computer to get just 1 second of biological brain processing time. While running, the simulation ate up about 1PB of system memory as each synapse was modeled individually.
Computing power will continue to ramp up while transistors scale down, which could make true neural simulations possible in real-time with supercomputers.
SpiNNaker is a manycore computer architecture designed to simulate the human brain. It is planned to use 1 million ARM processors (currently .5 million). The completed design will hold 100,000 cores
In this video, they showed a completed rack with 100,000 cores emulating 25 million neurons (at $\frac{1}{4}$ the efficiency—it will eventually run 1,000 neurons per core).