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Communications in Mathematical Physics

, Volume 227, Issue 3, pp 587–603 | Cite as

Simulation of Topological Field Theories¶by Quantum Computers

  • Michael H. Freedman
  • Alexei Kitaev
  • Zhenghan Wang

Abstract:

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models” having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H≡ 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold:

1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model “BQP”.

2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm.

Keywords

Tensor Product Quantum Computer Internal State Space Quantum Algorithm Quantum 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
  • Alexei Kitaev
    • 1
  • 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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