  The Pfaffian state, which may describe the quantized Hall plateau observed at
Landau level filling fraction $\nu = 5/2$, can support topologically-protected
qubits with extremely low error rates. Braiding operations also allow perfect
implementation of certain unitary transformations of these qubits. However, in
the case of the Pfaffian state, this set of unitary operations is not quite
sufficient for universal quantum computation (i.e. is not dense in the unitary
group). If some topologically unprotected operations are also used, then the
Pfaffian state supports universal quantum computation, albeit with some
operations which require error correction. On the other hand, if certain
topology-changing operations can be implemented, then fully
topologically-protected universal quantum computation is possible. In order to
accomplish this, it is necessary to measure the interference between
quasiparticle trajectories which encircle other moving trajectories in a
time-dependent Hall droplet geometry.
