Computación Cuántica Topológica y Sistemas Fuertemente Correlacionados

H. Bombín, Miguel Ángel Martín-Delgado


We introduce the basic notions describing topological quantum error correction codes and its extension to quantum computation. The underlying physical systems are strongly correlated systems of particles showing a topological order. These orders canbe described by quantum Hamiltonians defined on lattices such that the degeneration of the ground state depends on the lattice topology. For D=2 we show that a family of triangular codes allows us to implement the whole Clifford group in a transversal way. For D=3 we can even implement universal quantum computation in a transversal way using tetrahedral codes. Each of these codes gives rise to topological orders with very interesting features.

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