since I've investigated quite a bit about the topic recently, I think I ought to answer.
The short answer is: Ubuntu 16.04 with Unity is ready for 4k, with many limitations and various hardware restrictions.
If you want to stay sure you won't get serious issues, I'd go for a desktop computer with a single 4k monitor; make sure you install a recent Nvidia GPU with DP1.2 output. I have personally tested this setup with an Nvidia GTX 750, binary nvidia driver, DP output, single Philips BDM4065UC 4k monitor, and it works totally fine 3840x2160@60Hz ; you can pick 1.5 or 2.0 monitor scaling (aka 'retina adjustment'), depending on your taste. I've found everything was smooth and working without issues.
What I've found much harder to work with is:
- multiple monitors: especially if they're different and especially if you'd like a different scaling on different monitors; dragging windows around such monitors creates strange bugs. Maybe with identical 4k monitors the situation is better, but I wasn't able to test such scenario.
- laptops: I've yet to find a recent laptop working properly with an external 4k monitor (see Which laptop for Ubuntu 16.04 with 4k external monitor?), but many have succeeded at working properly with internal 4k monitors (e.g. I've heard about success with Dell XPS 9350 QHD).
UPDATE FOR 18.04
I'd say that stock 18.04 is a bit less 4k ready than 16.04. I suppose that Unity worked a bit better than Gnome with HiDpi. In 18.04, you can only choose between 200% and 300% scaling, scaled images look blurry, and some apps will just fail to pickup the scaling setting; also, the desktop feels quite laggy when scaling is enabled, even when using a dedicated GPU (both NVidia and AMD graphics was tested), and most window menus and icons will look blurred or pixelated when using scaling. A step back.
On the other hand, AMD GPUs seem to work out of the box with no proprietary driver. I tested RX550 and RX560, they worked properly with a LG 43UD79B monitor.