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Quantum computation and the localization of modular functors. (English) Zbl 1004.57026
To build a topological quantum computer, we need to find a real quantum system modeled by a modular functor. If such quantum systems do exist in nature, they should be described by some local Hamiltonian. In the paper under review, the author demonstrates the feasibility by designing a local Hamiltonian for the Witten-Chern-Simons theory at the 5th root of unity. Although the Hamiltonian is complicated, the theoretical implication is very significant. The general problem of localizing modular functors is still open. Further progress has been made by the author [A magnetic model with a possible Chern-Simons phase, Comm. Math. Phys. (to appear)].

MSC:
57R56 Topological quantum field theories (aspects of differential topology)
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
81P68 Quantum computation
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