Strong Resilience of Topological Codes to Depolarization
H. Bombin, Ruben S. Andrist, Masayuki Ohzeki, Helmut G. Katzgraber, M. A. Martin-Delgado · Physical Review X · 2012
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise.We compute the stability of the toric code to depolarization by mapping the quantum problem onto a classical disordered eight-vertex Ising model.By studying the stability of the related ferromagnetic phase via both large-scale Monte Carlo simulations and the duality method, we are able to demonstrate an increased error threshold of 18.9(3)% when noise correlations are taken into account.Remarkably, this result agrees within error bars with the result for a different class of codes-topological color codes-where the mapping yields interesting new types of interacting eight-vertex models.