When talking about near term quantum computing, one necessarily stumbles accross variational quantum algorithms. These algorithms have several issues when trying to implement them, and of the most discussed ones are barren plateaus. Here are a few basic results about them to get you started.
Perturbative gadgets are a tool that puts the traditional perturbation theory on its head and design a perturbation to create a desired system, instead of understanding a given perturbation on a given system Here is just a small recap of what I learned about them. Mainly a bit of history, how they are a fascinating contruct, and how they are tricky to work with.