Complexity Theory of BQP and PH
Recently Raz and Tal put out a great paper titled Oracle Separation of BQP and PH concerning the two complexity classes. There are a few good blog posts explaining what is going on, but in essence this is a theoretical paper relating quantum computing to topics similar to the P=NP region of theoretical computer science.
Somehow I also convinced my group members in my complexity theory class to present on this for our final project, which went pretty well despite being perhaps out of depth for what the class was about. Here is the presentation and a small report I wrote going in to more detail about how they got their results.