Context: Ed. Witten recently wrote a potentially revolutionary paper where he showed that under certain conditions, a Chern-Simons path integral in three dimensions is equivalent to an N = 4 path integral in four dimensions (this is the standard d=4, N=4 super Yang Mills theory)
Speculation: Witten had shown that the Chern-Simons topological quantum field theory can be solved in terms of Jones polynomials. A quantum computer can simulate a TQFT, and thereby approximate the Jones polynomial. (source: Wikipedia and this paper) Now I haven't completed reading Witten's paper and I wouldn't understand much of it anyways. But the idea is that if a quantum computer can simulate a path integral (or a Chern-Simons TQF) and since now Witten has shown in both of them to be dual descriptions in some sense, a quantum computer, atleast theoritically might be able to simulate a QFT. Also by the extension of that, Maldacena proposed that the specific field theory that Witten is using to be dual to type-II B string theory in AdS/CFT so then it may also be possible (only theoritically) to simulate a string theory.
Question: What are the technical constrains that a quantum or classical computer faces while simulating a QFT? Also my speculations only partially complete, could experts suggest a better description? Thanks!
PS. Also thanks to Mitchell Porter who brought up that paper before.