A modular functor which is universal for quantum computation

Zhenghan Wang

The topological modular functor from Witten-Chern-Simons theory is shown to be universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwined action of a braid on the functor's state space. A computational model based on Witten-Chern-Simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model.

created Thu Mar 2 12:57:22 PST 2000