Do you think computers will continue to advance, or will they at a certain point reach a limit?

Gordon Moore, an American engineer and cofounder of Intel, in a 1965 paper noted that the number of components in an integrated circuit appeared to double each year. This observation, after Moore updated it in 1975 to predict doubling every two years, became known popularly as "Moore's law," and for almost fifty years has held true as the power of chips of a given size has doubled annually.
In 2015, however, this trend ran into two major problems of physics. The first is that the more electronic components are placed in small a space, the harder it is to provide adequate cooling. The second problem is an effect known as "quantum tunneling," in which it becomes increasingly hard to direct the flow of electrons carrying information as components become smaller, since particles will probabilistically "tunnel" through barriers. Component sizes in recent chips are so small that additional shrinkage would exacerbate this problem.
What the end to Moore's law suggests is that we may be close to the end of our ability to incrementally develop existing technology and that future innovations in computing power will rely on new forms or applications of technology. Massively parallel forms of processing can provide performance increases with existing chip sets. Quantum computing and other new technologies looming on the horizon may eventually provide far more powerful hardware than we now have.