A Modular Functor Which is Universal¶for Quantum Computation
- Cite this article as:
- Freedman, M., Larsen, M. & Wang, Z. Commun. Math. Phys. (2002) 227: 605. doi:10.1007/s002200200645
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We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern–Simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model. The chief technical advance: the density of the irreducible sectors of the Jones representation has topological implications which will be considered elsewhere.