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.
The URL pointed to this text after it was shut down:
Hi there – thanks for your interest in our phone-based login experiment.
While we have concluded this particular experiment, we constantly experiment with new and more secure authentication mechanisms.
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'.