  We consider an extension to the geometric amoebot model that allows amoebots
to form so-called \emph{circuits}. Given a connected amoebot structure, a
circuit is a subgraph formed by the amoebots that permits the instant
transmission of signals. We show that such an extension allows for
significantly faster solutions to a variety of problems related to programmable
matter. More specifically, we provide algorithms for leader election,
consensus, compass alignment, chirality agreement and shape recognition. Leader
election can be solved in $\Theta(\log n)$ rounds, w.h.p., consensus in $O(1)$
rounds and both, compass alignment and chirality agreement, can be solved in
$O(\log n)$ rounds, w.h.p. For shape recognition, the amoebots have to decide
whether the amoebot structure forms a particular shape. We show how the
amoebots can detect a parallelogram with linear and polynomial side ratio
within $\Theta(\log{n})$ rounds, w.h.p. Finally, we show that the amoebots can
detect a shape composed of triangles within $O(1)$ rounds, w.h.p.
