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I will describe the principles of fault-tolerant quantum computing, and
explain why topological approaches to fault tolerance seem
especially promising. A two-dimensional medium that supports
abelian anyons has a topological degeneracy that can exploited for robust
storage of quantum information. A system of n nonabelian anyons in
two-dimensions has an exponentially large topologically protected Hilbert
space, and quantum information can be processed by braiding the
anyons. I will discuss in detail two cases where nonabelian anyons can
simulate a quantum circuit efficiently: fluxons in a "nonabelian
superconductor," and "Fibonacci anyons" with especially simple
fusion rules.
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