On the experimental side, the construction of a working, general-purpose quantum computer is what we are all hoping for. With luck, and with the help of recent theoretical advances, this may take a lot less than 50 years. It would be important not so much for its applications (which would be significant but rather specialised, such as code-breaking and the simulation of quantum-mechanical systems) but because it would be an entirely new way of harnessing nature. Some physicists, myself included, believe that even present-day quantum technology relies on the sharing of information-processing tasks between parallel universes.
On the theoretical side, I expect a further major integration between physics and information science. The key breakthrough would be the development of a quantum theory of construction – the general theory of what, according to the laws of physics, can or cannot be built and with what resources. If only we had such a theory today: it could tell us how hard it will be to build a quantum computer.