If you are in Canada, there is a way to finagle LTE onto the Nexus 4, according to the guys at XDA-Developers. Sadly, it only works in Canada, so the rest us are left out of this one. If you are in Canada, by simply entering a code hidden away in the phone you can LTE speeds. It almost seems too easy, but multiple users in Canada have tried it, and are showing data speeds that are right on par with you would expect to see from a 4G connected phone.
So far, the trick has been shown to work on Rogers and Telus in Canada. A user in our forums was able to get it going and broke it down step by step. Step by step might actually be over stating what you need to do, because it really is only a couple of steps.
All you have to do is go to the phone app on the device and enter a short code. The code is *#*#4636#*#*. After that, go to the Phone Information screen and click LTE Only from the menu. If you are on Rogers, you may have to enter the following APN:
Name - Rogers LTE
MMS Proxy- 10.128.1.69
Apn type 1- (default,supl,mms)
Of course, you can feel free to try it out in other regions, but so far, no one has made it work outside of Canada. If you manage to get it going somewhere else, make sure to hit the comments section and let us know.