Quantum Computation and the Localization of Modular Functors
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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.
AMS ClassificationPrimary 57R56 Secondary 68Q05, 81Q70, 82B10, 94B99, 20F36
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