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 paper 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. 
S. H. Simon, N.E. Bonesteel, M. H. Freedman, N. Petrovic, L. Hormozi