Topological quantum memory

@article{Dennis2002TopologicalQM,
  title={Topological quantum memory},
  author={Eric Dennis and Alexei Y. Kitaev and Andrew J. Landahl and John Preskill},
  journal={Journal of Mathematical Physics},
  year={2002},
  volume={43},
  pages={4452-4505}
}
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is… 
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