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Strong resilience of topological codes to depolarization



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Bombin, H. and Ruben, S. Andrist and Masayuki, Ohzeki and Katzgraber, Helmut G. and Martín-Delgado Alcántara, Miguel Ángel (2012) Strong resilience of topological codes to depolarization. Physical review X, 2 (2). ISSN 2160-3308

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Official URL: http://dx.doi.org/10.1103/PhysRevX.2.021004


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.

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©2012 All authors. We would like to thank H. Nishimori and D. Poulin for useful discussions. M. A. M.-D. and H. B. thank the Spanish MICINN Grant No. FIS2009-10061, CAM research consortium QUITEMAD Grant No. S2009-ESP1594, European Commission PICC: FP7 2007-2013, Grant No. 249958, UCM-BS Grant No. GICC-910758. Work at the Perimeter Institute is supported by Industry Canada and Ontario MRI. H. G. K. acknowledges support from the Swiss National Science Foundation (Grant No. PP002-114713) and the National Science Foundation (Grant No. DMR-1151387). M. O. acknowledges financial support from Grant-in-Aid for Young Scientists (B) No. 20740218 by MEXT and Kyoto University’s GCOE Program Knowledge-Circulating Society. The authors acknowledge ETH Zurich for CPU time on the Brutus cluster and the Centro de Supercomputación y Visualisación de Madrid (CeSViMa) for access to the Magerit-2 cluster.

Uncontrolled Keywords:8-Vertex model; Lattice model; Ising-model; Spin-glass; Quantum; entanglement; Statistics; Memory.
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:47734
Deposited On:29 May 2018 10:51
Last Modified:29 May 2018 10:51

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