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Topological quantum computation

2002; American Mathematical Society; Volume: 40; Issue: 1 Linguagem: Inglês

10.1090/s0273-0979-02-00964-3

1088-9485

Michael Freedman, Alexei Kitaev, Michael Larsen, Zhenghan Wang,

Quantum many-body systems

The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possibility for the realization of quantum computers. The chief advantage of anyonic computation would be physical error correction: An error rate scaling like e − α ℓ e^{-\alpha \ell } , where ℓ \ell is a length scale, and α \alpha is some positive constant. In contrast, the “presumptive" qubit-model of quantum computation, which repairs errors combinatorically, requires a fantastically low initial error rate (about 10 − 4 10^{-4} ) before computation can be stabilized.