DARPA and others are concernced about this exact scenario and are funding research into reverse-engineering chips to detect these types of backdoors. There are two parts this problem. One part is using electron microscopes and lasers and whatnot to go from silicon to a netlist of gates. The second part, which I'm a little more familiar with, is "decompiling" these gates into higher-level structures like ALUs and multipliers. The hope is that we can identify maybe 80% of the circuit to be good/recognized using purely algorithmic techniques and then a human can dig in and look through the remaining 20% for anything suspicious.

They do seem to be more concerned about chips the US buys from certain other countries than about the likes Intel/AMD building in backdoors.

EDIT: I should also mention that this is not just a concern of the american defence. I'm aware of the indian govt also funding this sort of research with similar motivation. However, in this instance, the professor was trying to attack the problem through the lens of formal techniques. I think the idea was to prove that if the chip interacts with the outside world through these limited set of channels then you can't sneak data out through some sort of covert channel hiding in the "regular" communication. The specific concern here was about routers/switches and the like equipment sneaking sensitive data out of a secure network.