**Quantum computing with topological qubits**

**Abstract:**A topological quantum computer is a hypothetical device in which intrinsic fault-tolerance is embedded in the hardware of the quantum computer. It is envisioned that in these devices quantum information will be stored in certain topologically-ordered states of matter and quantum computation will be carried out by braiding the world-lines of quasiparticle excitations that obey non-Abelian statistics, around one another, in specific patterns. I will review some of the properties of these states, and describe a general method for finding braiding patterns that correspond to a universal set of quantum gates on encoded topological qubits, based on quasiparticles that can be realized as excitations of certain fractional quantum Hall states.