Simulation of Topological Field Theories by Quantum Computers
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.
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.Attached Files
Submitted - FREcmp02preprint.pdf
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2011-10-10Created from EPrint's datestamp field
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