Comment by necubi

For hardware based sorting, we can do even better using sorting networks[0]. Sorting networks are comprised of a system of wires, one for each input, and comparators between wires which always output the higher number on the bottom wire and the lower on the top. Using this framework we can do massively parallel sorts with excellent time complexity.

The problem is that sorting networks need to be designed for each input size, and designing efficient sorting networks is an open problem. There has been some work in the evolutionary computing community on sorting networks, and some of the best known networks for various sizes were found by EAs, but large networks are still a challenge.

[0] http://en.wikipedia.org/wiki/Sorting_network