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Simulation of Topological Field Theories by Quantum Computers

Freedman, Michael H. and Kitaev, Alexei and Wang, Zhenghan (2002) Simulation of Topological Field Theories by Quantum Computers. Communications in Mathematical Physics, 227 (3). pp. 587-603. ISSN 0010-3616. doi:10.1007/s002200200635.

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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.

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Wang, Zhenghan0000-0002-5253-6400
Additional Information:© 2002 Springer-Verlag. Received: 4 May 2001; Accepted: 16 January 2002. Communicated by P. Sarnak. We would like to thank Greg Kupperberg and Kevin Walker for many stimulating discussions on the material presented here.
Issue or Number:3
Record Number:CaltechAUTHORS:20111007-112002181
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Official Citation:Freedman, M., Kitaev, A. & Wang, Z. Commun. Math. Phys. (2002) 227: 587. doi:10.1007/s002200200635
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27126
Deposited By: Tony Diaz
Deposited On:10 Oct 2011 21:40
Last Modified:09 Nov 2021 16:46

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