Publication: Tricolored lattice gauge theory with randomness: fault tolerance in topological color codes
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We compute the error threshold of color codes—a class of topological quantum codes that allow a direct implementation of quantum Clifford gates—when both qubit and measurement errors are present. By mapping the problem onto a statistical–mechanical three-dimensional disordered Ising lattice gauge theory, we estimate via large-scale Monte Carlo simulations that color codes are stable against 4.8(2)% errors. Furthermore, by evaluating the skewness of the Wilson loop distributions, we introduce a very sensitive probe to locate first-order phase transitions in lattice gauge theories.
© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We thank A P Young for useful discussions. MAM-D and HB acknowledge financial support from research grant QUITEMAD S2009-ESP-1594, FIS2009-10061, UCM-BS/910758 and EU grant PICC. HGK acknowledges support from the SNF (grant no. PP002-114713). The authors acknowledge ETH Zurich for CPU time on the Brutus cluster and the Centro de Supercomputación y Visualización de Madrid (CeSViMa) for access to the Magerit cluster.