The initial stages of a sigmoid curve resemble exponential growth. I'm pretty sure that the exponential character we've witnessed is the result of miniaturization of the transistor and the industrialization of large third-world economies, both of which are running out of steam. If we don't get some major new breakthroughs, expect to see the other side of that sigmoid soon enough.

We may see another brief exponential curve with the development of carbon nano-computers, likely netting at least an order of magnitude additional computing performance. I have strong doubts about the feasibility of general purpose quantum computing (though it will definitely have niche uses).