Computación Cuántica Topológica y Sistemas Fuertemente Correlacionados

Resumen

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.