The notion of quantum topological order has been a subject of much interest recently, in part because it falls outside of the well-established Landau paradigm whereby states of matter are classified according to their broken symmetries. Topologically ordered phases cannot be described by any local order parameter, yet they have many peculiar properties clearly distinguishing them form the conventionally disordered phases. For example, in two dimensions, they may support anyonic excitations - the quasiparticles that are neither bosons nor fermions. Moreover, anyons with *non-Abelian* braiding statistics are expected to occur, particularly in the fractional quantum Hall regime.

Interesting in their own right, such systems may also provide a platform for topological quantum computation.  Interferometric experiments are likely to play a crucial role in both determining the non-Abelian nature of these states and in their potential applications for quantum computing. I will discuss solid state interferometers designed to detect such non-Abelian quasiparticle statistics. Should these experiments succeed, such interferometers could also become key elements in a topological quantum computer.