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. 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.