(Which does not make that technology, mind you, any less cool. But it's different enough from traditional photography that I thought it was worth mentioning.)
A sphere 1km across has a surface are of 4pi1km^2 which is roughly 10^7m^2. If you had 1cm^2 sensors then you get 10^4 sensors per m^2, which means you get 10^11 sensors total. At 11k fps (10^4) that's a total of 10^15 fps.
Note that Planck time is 10^-44 so such an arrangement probably wouldn't help for detecting quantum gravity because you'd run out of matter in the universe before you could construct the sensors.
Let's start off with a baseline image resolution of 1 megapixel.
1 Joule is about 6E18 visible light photons, give or take. So that's then 6E12 photons per pixel.
Full sunlight on Earth has an intensity of around 1400 Watts (Joules/second) per square meter, or 0.14 Watts per square cm.
So achieving a frame rate in the trillions of fps would likely run into some limits relative to the size of your optics, the intensity of light coming from the scene, or the bulk quantum efficiency of the sensor.
And, of course, if you try to achieve quintillions of fps then you start dumping in nearly an entire Watt in photons into every single pixel on your sensor, which rapidly becomes a very big problem re: everything melting.
Additionally, modern electronics has trouble operating above the low GHz range, beyond that you'd need to move to superconductors or some such to keep up with the data.
The title of my link says 'single-shot'. The underlying Nature article at http://www.nature.com/nature/journal/v516/n7529/full/nature1... says "Here we demonstrate a two-dimensional dynamic imaging technique, compressed ultrafast photography (CUP), which can capture non-repetitive time-evolving events at up to 10^11 frames per second"
These can do 25k fps at 1280x800 pixels (and 1 million fps at 128x32 pixels): http://www.visionresearch.com/Products/High-Speed-Cameras/UH...
That got me thinking, is there any theoretical limit to the number of frames that can be captured in one second?