Andrist, Ruben S.Katzgraber, Helmut G.Bombin, H.Martin-Delgado Alcántara, Miguel Ángel2023-06-202023-06-202011-08-081367-263010.1088/1367-2630/13/8/083006https://hdl.handle.net/20.500.14352/42824© 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.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.engjournal articlehttp://dx.doi.org/10.1088/1367-2630/13/8/083006http://iopscience.iop.orgopen access53Error-correcting codesQuantum memoryModel.Física-Modelos matemáticos