Even a brand-new Macbook would be unable to power this display. All currently sold Macbooks can only power displays up to 2560 by 1600; the Macbook Air can power one external display at this resolution, and the Macbook Pro can power two. (Edit: The iMac can also only power one additional display at the same resolution.)
If you want to use a Mac with a 4K display, consider getting a Mac Pro, which can power up to three of them.
While the integrated graphics on the 2013 models can drive 4k displays at 60fps, only Thunderbolt 2 has the necessary bandwidth. The latest rMBPs have Thunderbolt 2, so they should be fine once OS X's drivers are updated. Everything else is stuck at 30fps.
If you want to use a Mac with a 4K display, consider getting a Mac Pro, which can power up to three of them.