Topological Quantum Computing with Only One Mobile Quasiparticle

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. 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. This result may greatly reduce the technological challenge of realizing topological quantum computation.