Google already did this (in part), it was called 'Sesame' and allowed you to log in to your Google account (on a desktop browser) by scanning a on-screen QR code with your phone.

However it was apparently just an experiment, and unfortunately has been shut down.

For a bit more info: http://www.webpronews.com/open-sesame-googles-newest-securit...

Or just search for 'Google Sesame'.