No, I don't think that QCs will help much for simulating chaotic systems, except insofar as those systems are also quantum-mechanical. For (e.g.) predicting the weather, there may be small quantum speedups that you can get here and there, from Grover's algorithm and faster gradient computation and so forth, but at a fundamental level, as far as anyone knows, you still need to just iterate the partial differential equation from one time step to the next, same as a classical computer does.
Stepping back, note that "quantum" and "nonlinear" are two completely different concepts -- in fact, at the level of amplitudes (i.e., the Schrodinger equation), quantum mechanics is the one example we have in physics of a perfectly LINEAR theory! Alan Sokal had a lot of fun with that point in his "Social Text" parody article: http://www.physics.nyu.edu/sokal/transgress_v2/transgress_v2...
On the other hand, this is perfectly compatible with quantum systems having chaotic phenomena at the level of observables (like the positions and momenta of particles), and in fact there's a whole field called "quantum chaos" that studies such situations.
Stepping back, note that "quantum" and "nonlinear" are two completely different concepts -- in fact, at the level of amplitudes (i.e., the Schrodinger equation), quantum mechanics is the one example we have in physics of a perfectly LINEAR theory! Alan Sokal had a lot of fun with that point in his "Social Text" parody article: http://www.physics.nyu.edu/sokal/transgress_v2/transgress_v2...
On the other hand, this is perfectly compatible with quantum systems having chaotic phenomena at the level of observables (like the positions and momenta of particles), and in fact there's a whole field called "quantum chaos" that studies such situations.