Unfortunately I'm not able to update Charlie's post so I thought it was worth re-posting the latest news.
According to Pirates GM Neal Huntington, "A.J. will work through the three-step return to pitch progression. The initial step will be to heal from the surgery. Secondly we will recondition his arm and body to where he was prior to the injury. Lastly, we will put A.J. through the same progression as he would have gone through here in spring training. The very rough timetable to complete this process and have A.J. prepared to compete without restrictions at the Major League level is 8-12 weeks."
This likely means Burnett will be back in early to mid-May and likely miss 5-7 starts.