You heard it here first.
Today’s supercomputers (and most datacenters) now use considerable power for their operation, and those supercomputers typically only run in the tens to hundreds (~130) of petaflops (varies depending on the benchmark used). They consume in the 2.2 to 17 megawatts of power to run them (as of June 2017). If we extrapolate (using the same technology used in those supercomputers) that to the exaflop range, we will be using perhaps in the gigawatts range (bear in mind that with new generations of technologies power usage is often reduced) . Datacenters often use much more power and their aggregate computation rates (corresponding petaflops) are much higher also. These figures are specific to the computation machines and do not include the additional cooling, heating, and other ancillary power consumption.
Nuclear military vehicles (e.g. nuclear submarines) create on the order of a few tens to hundreds of megawatts. Commercial reactors generate upwards of ~1.5 gigawatts.
The Hayden postulate consists of Thorium based nuclear power (“Thorium in“) for driving computers that run at the exaflops (>1000 petaflops) scale (“exaflops out“).
Sources:
Top Supercomputer speed and power usage ratings:
Thorium information sources:
Current and Future Based Thorium
How Much Energy All US Data Centers Consume