Canonical has released a very early edition of Ubuntu on the Nexus 7. This one is aimed at developers and offer ways to install a build of Ubuntu on the Google Nexus 7 Tablet.
Using this tool, you can download and install a test build on your Nexus 7 device. This would require the boot loader of your device to be unlocked.
The app seems to support all the variants including the 8GB one. Though it is not recommended if you have no idea what you are getting into.
Ubuntu is still far away from featuring a user interface optimized for touchscreen devices so do not expect it to be usable for regular purposes.
ASUS Nexus 7
Canonical Ubuntu 12.04