The idea, and this can be seen on DARPA's slides (http://www.darpa.mil/workarea/downloadasset.aspx?id=21474857...), is to get computation that is several orders of magnitude higher for their specialized sets of problems than what can theoretically be reached by traditional computing models even if Moore's law continues.
DARPA would like to first apply this technology to ARGUS drone systems (https://www.youtube.com/watch?v=QGxNyaXfJsA) and related technology because streaming video can't be done to the ground, tracking and decision making must be done on board - yet traditional processing platforms can only track a few orders of magnitude fewer targets that what the military would like.
In a more advanced phase, if memristor or coupled oscillator (etc) approaches to building inference models become possible, then programs written in DARPA's other initiative (Probablistic Programming) could be programmed into these exotic solid state devices to compute in a way more analogous to today's generic computation. And indeed, eventually the adoption of Probablistic Programming will train programmers to write code for quantum computers - while more complicated, replacing Probablistic Programming's PDFs with probability amplitudes almost get one there.
I hope to see more journalistic coverage of some of the other exotic devices.