Topological Quantum Computing with Only One Moving Quasiparticle

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