Quantum Computation and the Localization of Modular Functors
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- Freedman, M.H. Found. Comput. Math. (2001) 1: 183. doi:10.1007/s102080010006
The mathematical problem of localizing modular functors to neighborhoods of points is shown to be closely related to the physical problem of engineering a local Hamiltonian for a computationally universal quantum medium. For genus =0 surfaces, such a local Hamiltonian is mathematically defined. Braiding defects of this medium implements a representation associated to the Jones polynomial and this representation is known to be universal for quantum computation.