2000/01/31 by Michael H. Freedman, Alexei Kitaev, Zhenghan Wang · 2 citations
Mathematics · Physics and Astronomy · #math.GT #quant-ph
paper · pdf · doi:10.1007/s002200200635
published as Commun.Math.Phys. 227 (2002) 587-603
arxiv created 2000/03/17 · arxiv updated 2009/11/30
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 filed 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.