String theory exploits this analogy by replacing the Feynman diagrams of ordinary quantum field theory with 2-dimensional cobordisms, which represent the worldsheets traced out by strings with the passage of time. The analogy between operators and cobordisms is also important in loop quantum gravity and — most of all — the more purely mathematical discipline of ‘topological quantum field theory’.
Meanwhile, quite separately, logicians had begun using categories where the objects represent propositions and the morphisms represent proofs. The idea is that a proof is a process going from one proposition (the hypothesis) to another (the conclusion). Later, computer scientists started using categories where the objects represent data types and the morphisms represent programs. They also started using ‘flow charts’ to describe programs. Abstractly, these are very much like Feynman diagrams!
The logicians and computer scientists were never very far from each other. Indeed, the ‘Curry–Howard correspondence’ relating proofs to programs has been well-known at least since the early 1970s, with roots stretching back earlier.
‒ John C. Baez and Mike Stay, https://arxiv.org/pdf/0903.0340.pdf