Papers on using resource states to implement QFT efficiently
Here is a 2018 paper that uses phase gradient states and adders to optimize the T-count of the approximate QFT: "Approximate Quantum Fourier Transform with O(nlog(n)) T gates" by Nam et al.

(The careful reader may notice that the question precedes the paper by two years! That's because the question actually led to the paper, though indirectly. I mentioned the phase gradient operation as an application of efficient adders in this paper, Nam et al saw that, independently realized it would useful for the approximate QFT, and here we are full circle. Oh, and of course Kitaev scooped everyone by over ten years. He mentions the adding-into-phase-gradient technique in a textbook from 2002 [page 133].)