What makes these fictional devices useful for understanding the real world? In brief, they can reveal hidden connections between different complexity classes.
Take the two most famous complexity classes. There’s the class of problems that are easy to solve, which researchers call “P,” and the class of problems that are easy to check, which researchers call “NP.” Are all easy-to-check problems also easy to solve? If so, that would mean that NP would equal P, and all encryption would be easy to crack (among other consequences). Complexity theorists suspect that NP does not equal P, but they can’t prove it, even though they’ve been trying to pin down the relationship between the two classes for over 50 years.