4K video support is still pretty new, and it can be costly to get for your home theatre. Your computer is another story. With a decent enough graphics card and monitor, all you need is content. YouTube can provide that with Google's Testtube program.
Much like Google Labs in other Google properties, Testtube allows adventurous users to try out new YouTube features. Currently, there are only two features. One is a new YouTube player (which we've already shown you how to activate on your own), and the other is 4K video support.
With this activated, users can stream 4K video in up to 60fps where available. Google even has a selection of videos you can start with. It won't solve the problem of waiting for your favourite shows to come in 4K flavours, but you can at least start testing out how your machine handles it.