Large k topological quantum computer

Abstract

Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory and used for quantum computations. Quantum qudit gates of this quantum computer are represented by sequences of quantum R-matrices. Its dimension and explicit form depend on the parameters of the Chern-Simons theory — level k, gauge group SU(N), and representation, which is chosen to be symmetric representation [r]. In this paper, we examine the universality of such a quantum computer. We prove that for sufficiently large k it is universal, and the minimum allowed value of k depends on the remaining parameters r and N.