I have the late 2011 Asus Zenbook (I think it's an UX31E, can't check right now, my girlfriend is watching a cooking show on it...) and I'm running ubuntu 12.10 (and previsouly 12.04 pre-release and release). It's running fine. Especially now the needed drivers and ACPI fixes are into mainline kernel.
I can get up to 6h of battery use (brigthness 50%, wifi off) using sublime text and listening to music with earbuds. I used to have poor wifi reecption but seems a thing of the past *knock wood*.