Quantum Computation and the localization of Modular Functors

Details Quantum Computation and the localization of Modular Functors Quantum Computation and the localization of Modular Functors

2000-03-28

arxiv.org/abs/quant-ph/0003128v5

Physics

Quantum Physics

Scientific paper

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.

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