Communications in Mathematical Physics

, Volume 227, Issue 3, pp 605–622

A Modular Functor Which is Universal¶for Quantum Computation

  • Michael H. Freedman
  • Michael Larsen
  • Zhenghan Wang

DOI: 10.1007/s002200200645

Cite this article as:
Freedman, M., Larsen, M. & Wang, Z. Commun. Math. Phys. (2002) 227: 605. doi:10.1007/s002200200645

Abstract:

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael H. Freedman
    • 1
  • Michael Larsen
    • 2
  • Zhenghan Wang
    • 2
  1. 1.Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399, USAUS
  2. 2.Indiana University, Dept. of Math., Bloomington, IN 47405, USAUS

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