It's beautiful but if I didn't already know what the Q logo stood for I'd be very confused as to what it exactly it refers to.

More specifically, I think the squareness of the Q would tell me that it has something to do with a square but I wouldn't be able to make the mental leap from "square" to "squared".

For instance in the posters where you have a person inside the "Q" and say "He's a 'Q'." it makes me read "He's a square" which isn't a very nice thing to say about someone.