I had a quick look online for information on this and to my surprise Sony already have a 4K streaming service which they have said will eventually come to PS4.
The file sizes are huge though with a movie being at least 100GB. Better upgrade your hard drive and internet speeds if you want to watch 4K content.
I'm in a city that Google Fiber is coming to so I will hopefully be able to stream some 4k!
Lucky you, what speeds are you expecting from Google Fiber ? I'd imagine it would need to be extremely fast for 4K streaming.
A quote from wiki "Google Fiber will provide an Internet connection speed of one gigabit per second (1,000 Mbit/s) for both download and upload which is roughly 100 times faster access than what most Americans have. Google Fiber says its service allows for the download of a full movie in less than two minutes."
So yes, I'd hope it would be able to!
And I thought I was doing well with 70 Mbits/s. I doubt you'll have any problems with 4K or anything download related...ever.