It helps with simulation of quantum mechanics, but I don't think that it helps with most classical simulations.

As Eugine mentions, there is a concrete way to use time travel to solve NP problems, those where you can recognize the answer if you have it. In fact, it is possible, under one formalization, to use it to solve a class of problems called PSPACE, which just means problems that you could solve with unlimited time, but limited memory, the obvious guess when NoSuchPlace says "infinite time." But look up the method Eugine mentioned - it isn't obvious how to extend it.

I don't know any applications of PSPACE problems, because they are impractical, but NP problems come up all the time and there is a big industry of solving examples on the edge of practicality. People often do this by converting them to SAT, the universal NP problem and then apply "SAT solvers"; so googling something like "sat solver applications" gives various suggestions, such as microchip design. Of course, if you really could solve SAT problems, you'd use much larger examples that people don't even bother with today. And if you could really solve PSPACE problems, you'd try even more exotic things.