In topological quantum computation one aims to make use of quantum systems described by topological quantum field theory for quantum computation.
For the time being see at quantum computation for more.
Michael H. Freedman, Alexei Kitaev, Michael J. Larsen, Zhenghan Wang. Topological quantum computation, Bull. Amer. Math. Soc. 40 (2003), 31-38, web, pdf
M. Freedman, M. Larsen, and Z. Wang, A modular functor which is universal for quantum computation, Comm. Math. Phys. 227 (2002), no. 3, 605-622, pdf
Michael Freedman, Michael Larsen, Zhenghan Wang, A modular functor which is universal for quantum computation (arXiv:quant-ph/0001108)
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, Non-Abelian Anyons and Topological Quantum Computation, (arXiv:0707.1888)