Error threshold estimates for surface code with loss of qubits
Masayuki Ohzeki
Phys. Rev. A 85, 060301(R) (2012).
arXiv:1202.2593
First work in RomeWe estimate optimal thresholds for surface codes in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a finite-dimensional spin glass, which is disordered magnetic material. We compare our estimations to the heuristic numerical results reported in earlier studies. Further application of our method to the depolarizing channel, a natural generalization of the noise model, unveils its wider robustness even with loss of qubits.
Strong Resilience of Topological Codes to Depolarization
Hector Bombin, Ruben S. Andrist, Masayuki Ohzeki, Helmut G. Katzgraber and Miguel Angel Martin-Delgado
Phys. Rev. X, 2 (2012) 021004
arXiv:1202.1852
featured in Viewpoint (Physics 5, 50 (2012)) 
Researchers gather in SpainThe 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.
