That's really hard to tell without knowing how good in learning you are. I would bet some people could do it in a week (or course not the whole thesis, just to learn and make a working simple compute shader particle system). And many people wouldn't learn it in years.
Also, how flexible/universal should the system be? Is it supposed to have some kind of configuration (via a dialog or some "script" file) for different kinds of particle behaviour and appearance (flames, rain, show, smoke, sparks, missile trails etc)?
And against what are you planning to compare the performance advantage? Against a CPU particle system?