Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such
\nas protected quantum gates with relatively low overhead and robustness against imperfect mea-
\nsurement of error syndromes. Here we investigate the storage threshold error rates for bit-
\nip and
\nphase-
\nip noise in the 3D color code on the body-centererd cubic lattice, assuming perfect syndrome
\nmeasurements. In particular, by exploiting a connection between error correction and statistical
\nmechanics, we estimate the threshold for 1D string-like and 2D sheet-like logical operators to be
\np(1)
\n3DCC ‘ 1:9% and p(2)
\n3DCC ‘ 27:6%. We obtain these results by using parallel tempering Monte Carlo
\nsimulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical
\nmodels: the 4- and 6-body random coupling Ising models.<\/p>\n","protected":false},"excerpt":{"rendered":"
Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect mea- surement of error syndromes. Here we investigate the storage threshold error rates for bit- ip and phase- ip noise in the 3D color code on the body-centererd cubic lattice, assuming perfect 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