In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in $2+1$ dimensional space-time. In this Letter we show that any such quantum computation that can be done by braiding $n$ identical quasiparticles can also be done by moving a single quasiparticle around $n-1$ other identical quasiparticles whose positions remain fixed.

• Received 23 September 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.070503