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Communications in Mathematical Physics

, Volume 227, Issue 3, pp 605–622 | Cite as

A Modular Functor Which is Universal¶for Quantum Computation

  • Michael H. Freedman
  • Michael Larsen
  • Zhenghan Wang

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.

Keywords

State Space Computational Model Quantum Computation Technical Advance Circuit Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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