Recent graphics cards like the AMD Radeon HD 6000/7000 and NVIDIA GeForce GTX 600 series support 4K resolution outputs, but several Phoronix readers in recent weeks have written in (or tweeted) to ask about 4K Linux hardware support. I don't have a clear answer since presently there's no 4K monitor in our lab for testing with different GPUs/drivers, but recently there was a 4K monitor/driver discussion thread launched in our forums.
AMD's Alex Deucher responded about the open-source Radeon driver that if using DisplayPort it should work on the Radeon HD 6000 series or HDMI and DisplayPort connections on the Radeon HD 7000 series GPUs (or the Trinity APU too). The necessary DRM patches for properly dealing with 4K monitor modes were just merged into the Linux 3.12 kernel.
The binary AMD and NVIDIA graphics drivers meanwhile should support 4K monitors and their native resolutions too if using supported hardware. I haven't seen any commits for the Nouveau DRM pertaining to 4K modes (will update though if I hear differently) but for Intel hardware I believe there is also 4K monitor support in their latest DRM code.