There are some fanless GCN-Core Radeons that can output 4K over displayport 1.2, I've seen up to 7750 at least. Can't get much quieter than that.
True Kepler-Core Nvidia 6xx series cards also support it. (beware: on the low end both amd and nvidia do stupid rebranding of older cores with new numbers)
Honestly though by the time 4k screens are a reasonable price (several years) just about any gpu should be able to handle it fine.
My next computer screen upgrade will be 4k for sure but considering that is just becoming available at around 6 grand for 32", the 30" 1600p I got for 1k a few years back has a lot of life left in it.
Nearly dead silent HTPC ver 2.0: i3-4340 w/ Noctua NH-L9i on Z87E-itx inside CM130 elite, fanless PSU, SSD OS drive
SAN shares via 40GbE tunneled over 56Gb infiniband links
microcenter & ebay = severe risks to my wallet